Search results for: symbolic computation

Authors: Edris Rawashdeh, I. Abu-Falahah, H. M. Jaradat

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The variable-coefficient non-linear dispersive wave equation is investigated with the aid of symbolic computation. By virtue of a newly developed simplified bilinear method, multi-soliton solutions for such an equation have been derived. Effects of the inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed with the aid of the characteristic curve method and graphical analysis.

Keywords: dispersive wave equations, multiple soliton solution, Hirota Bilinear Method, symbolic computation

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Authors: N. Fusun Oyman Serteller

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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Muhammad Younis

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In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the modified Burgers’ equation with the aid of computation. The method is reliable and useful, which gives more general exact travelling wave solutions than the existing methods. These obtained solutions are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Some of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

Keywords: traveling wave solutions, NLPDE, computation, integrability

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Authors: Sherri Franklin-Guy

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Play activities have long been utilized to support the development of expressive language in young children. More specifically, stages of symbolic play, or pretend play, have served as indicators of levels of cognitive development, the foundation of language. This presentation will examine the relationship between symbolic play and language development in toddlers and preschoolers. Implications for clinicians and educators will be discussed.

Keywords: cognition, language development, pretend play, symbolic play

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Letizia Maria Drammis, Maria Antonella Brandimonte

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The idea that people use space representations to think about time and number received support from several lines of research. However, how these representations develop in children and then shape space-time and space-number mappings is still a debated issue. In the present study, 40 children (20 pre-schoolers and 20 elementary-school children) performed 4 main tasks, which required the use of more concrete (non-symbolic) or more abstract (symbolic) space-time and space-number associations. In the non-symbolic conditions, children were required to order pictures of everyday-life events occurring in a specific temporal order (Temporal sequences) and of quantities varying in numerosity (Numerical sequences). In the symbolic conditions, they were asked to perform the typical time-to-position and number-to-position tasks by mapping time-related words and numbers onto lines. Results showed that children performed reliably better in the non-symbolic Time conditions than the symbolic Time conditions, independently of age, whereas only pre-schoolers performed worse in the Number-to-position task (symbolic) as compared to the Numerical sequence (non-symbolic) task. In addition, only older children mapped time-related words onto space following the typical left-right orientation, pre-schoolers’ performance being somewhat mixed. In contrast, mapping numbers onto space showed a clear left-right orientation, independently of age. Overall, these results indicate a cross-domain difference in the way younger and older children process time and number, with time-related tasks being more difficult than number-related tasks only when space-time tasks require symbolic representations.

Keywords: space-time associations, space-number associations, orientation, children

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Authors: Haohao Wang

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The purpose of this paper is to find elimination ideals via Grobner basis. We first introduce the concept of Grobner bases, and then, we provide computational algorithms to applications for curves and surfaces.

Keywords: curves, surfaces, Grobner basis, elimination

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Authors: Ampai Muensit, Maniemai Thongyou, Patcharin Lapanun

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Teen mothers have been viewed as ‘a powerless’ facing numerous pressures including poverty, immaturity of motherhood, and especially social blame.This paper argues that, to endure as an agent, they keep struggling to overcome all difficulties in their everyday life by using certain symbols to negotiate the situations they encounter, and to obtain a social position without surrendering to the dominating socio-cultural structure. Guided by Bourdieu’s theory of practice, this study looks at how teen mothers use symbolic capital in their motherhood practices. Although motherhood practices can be found in different contexts with various types of capital utilization, this paper focuses on the use of symbolic capitals in teen mothers’ practices within the contexts of the community. The study employs a qualitative methodology; data was collected from 12 informants through life history, in-depth interview, observation and the content analytical method was employed for data analysis. The findings show that child and motherhood were key symbolic capitals in motherhood practices. Employing such capitals teen mothers can achieve an acceptance from community – particularly from the new community. These symbolic capitals were the important sources of teen mothers’ power to turn the tide by changing their status – from “the powerless” to be “the agent”. The use of symbolic capitals also related to habitus of teen mothers in better compromising for an appropriate social position.

Keywords: teen mother, motherhood practice, symbolic capital, community

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Authors: K. Umbleja, M. Ichino, H. Yaguchi

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In this paper, we propose a coloring method for multivariate data visualization by using parallel coordinates based on dissimilarity and tree structure information gathered during hierarchical clustering. The proposed method is an extension for proximity-based coloring that suffers from a few undesired side effects if hierarchical tree structure is not balanced tree. We describe the algorithm by assigning colors based on dissimilarity information, show the application of proposed method on three commonly used datasets, and compare the results with proximity-based coloring. We found our proposed method to be especially beneficial for symbolic data visualization where many individual objects have already been aggregated into a single symbolic object.

Keywords: data visualization, dissimilarity-based coloring, proximity-based coloring, symbolic data

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Authors: K. Umbleja, M. Ichino

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Symbolic data mining has been developed to analyze data in very large datasets. It is also useful in cases when entry specific details should remain hidden. Symbolic data mining is quickly gaining popularity as datasets in need of analyzing are becoming ever larger. One type of such symbolic data is a histogram, which enables to save huge amounts of information into a single variable with high-level of granularity. Other types of symbolic data can also be described in histograms, therefore making histogram a very important and general symbolic data type - a method developed for histograms - can also be applied to other types of symbolic data. Due to its complex structure, analyzing histograms is complicated. This paper proposes a method, which allows to compare two histogram-valued variables and therefore find a dissimilarity between two histograms. Proposed method uses the Ichino-Yaguchi dissimilarity measure for mixed feature-type data analysis as a base and develops a dissimilarity measure specifically for histogram data, which allows to compare histograms with different number of bins and bin widths (so called general histogram). Proposed dissimilarity measure is then used as a measure for clustering. Furthermore, linkage method based on weighted averages is proposed with the concept of cluster compactness to measure the quality of clustering. The method is then validated with application on real datasets. As a result, the proposed dissimilarity measure is found producing adequate and comparable results with general histograms without the loss of detail or need to transform the data.

Keywords: dissimilarity measure, hierarchical clustering, histograms, symbolic data analysis

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Authors: Yu Chen

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In line with existing philosophical approaches, this research proposes a conceptual model with an innovative spatial vision and aesthetic principles for Artificial Intelligence (AI) application in brand advertising. The model first identifies the major constituencies in contemporary advertising on three spatial levels—physical, psychological, and symbolic. The model further incorporates the relationships among AI, aesthetics, branding, and advertising and their interactions with the major actors in all spaces. It illustrates that AI may follow the aesthetic principles-- beauty, elegance, and simplicity-- to reinforce brand identity and consistency in advertising, to collaborate with stakeholders, and to satisfy different advertising objectives on each level. It proposes that, with aesthetic guidelines, AI may assist consumers to emerge into the physical, psychological, and symbolic advertising spaces and helps transcend the tangible advertising messages to meaningful brand symbols. Conceptually, the research illustrates that even though consumers’ engagement with brand mostly begins with physical advertising and later moves to psychological-symbolic, AI-assisted advertising should start with the understanding of brand symbolic-psychological and consumer aesthetic preferences before the physical design to better resonate. Limits of AI and future AI functions in advertising are discussed.

Keywords: AI, spatial, aesthetic, brand advertising

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Authors: Manuel Alves, Angelica Reis, Armindo Lobo, Valdemar Leiras

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In industry 4.0, it is common to have a lot of sensor data. In this deluge of data, hints of possible problems are difficult to spot. The digital twin concept aims to help answer this problem, but it is mainly used as a monitoring tool to handle the visualisation of data. Failure detection is of paramount importance in any industry, and it consumes a lot of resources. Any improvement in this regard is of tangible value to the organisation. The aim of this paper is to add the ability to forecast test failures, curtailing detection times. To achieve this, several anomaly detection algorithms were compared with a symbolic regression approach. To this end, Isolation Forest, One-Class SVM and an auto-encoder have been explored. For the symbolic regression PySR library was used. The first results show that this approach is valid and can be added to the tools available in this context as a low resource anomaly detection method since, after training, the only requirement is the calculation of a polynomial, a useful feature in the digital twin context.

Keywords: anomaly detection, digital twin, industry 4.0, symbolic regression

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Authors: Adarsh Shroff

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Big data is a collection of dataset so large and complex that it becomes difficult to process using data base management tools. To perform operations like search, analysis, visualization on big data by using data mining; which is the process of extraction of patterns or knowledge from large data set. In recent years, the data mining applications become stale and obsolete over time. Incremental processing is a promising approach to refreshing mining results. It utilizes previously saved states to avoid the expense of re-computation from scratch. This project uses i2MapReduce, an incremental processing extension to Map Reduce, the most widely used framework for mining big data. I2MapReduce performs key-value pair level incremental processing rather than task level re-computation, supports not only one-step computation but also more sophisticated iterative computation, which is widely used in data mining applications, and incorporates a set of novel techniques to reduce I/O overhead for accessing preserved fine-grain computation states. To optimize the mining results, evaluate i2MapReduce using a one-step algorithm and three iterative algorithms with diverse computation characteristics for efficient mining.

Keywords: big data, map reduce, incremental processing, iterative computation

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Authors: Yogita M. Ahire, Nedal M. Mohammed, Ahmed A. Hamoud

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Scientific computation outsourcing is gaining popularity because it allows customers with limited computing resources and storage devices to outsource complex computation workloads to more powerful service providers. However, it raises some security and privacy concerns and challenges, such as customer input and output privacy, as well as cloud cheating behaviors. This study was motivated by these concerns and focused on privacy-preserving Two-Point Boundary Value Problems (BVP) as a common and realistic instance for verifiable safe multiparty computing. We'll look at the safe and verifiable schema with correctness guarantees by utilizing standard multiparty approaches to compute the result of a computation and then solely using verifiable ways to check that the result was right.

Keywords: verifiable computing, cloud computing, secure and privacy BVP, secure computation outsourcing

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Authors: Rizwan Rizwan

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Secure Multiparty Computation is an emerging area of research within the cryptographic community, enabling secure collaboration among multiple parties while safeguarding their sensitive data. Secure Multiparty Computation has been extensively studied in the context of plane geometry, its application to complex solid geometry shapes remains relatively unexplored. This research paper aims to bridge this gap by proposing a solution for the secure multiparty computation of intersecting tetrahedra. We present an approach to calculate the volume of intersecting tetrahedra securely while preserving the privacy of the input data provided by each participating party. The proposed solution leverages accepted simulation paradigms to prove the privacy of the computation. We thoroughly analyze the computational and communication complexities of our approach, demonstrating that they closely align with the minimum theoretical complexity for the problems at hand. This optimal nature of our solution ensures efficient and secure collaborative geometric computations.

Keywords: cryptography, secure multiparty computation, solid geometry, protocol, simulation paradigm

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Authors: Victor Ademulegun Arijeniwa

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This is a sociolinguistic study of Olu Obafemi’s Naira Has No Gender as a microcosm of life experiences. The paper assesses how Olu Obafemi’s use of language in the dramatic world serves as both social relationships and symbolic order of communicative roadmap that are capable of yielding well expressed and richly articulated sociolinguistic implications. Being the interface between language and social institutions, sociolinguistics and its application is highly utilitarian in linguistics analysis, especially where the language of a text appears to be deeply tensed, such as found in dramatic texts. The aim of this paper has been (i) to assess the symbolic orderly presentation of form in Olu Obafemi’Naira Has No Gender; (ii) to find out the linguistic elements and textual organization that represent social relationships in Olu Obafemi’s Naira Has No Gender. Using qualitative research design in data generation with insights from John Gumperz Interactional Sociolinguistics Theory with particular reference to contextualization cues and miscommunication, the paper identifies the implication of the dramatic discourse on society.

Keywords: sociolinguistics, Microcosm, contextualisation, miscommunication variable, identity, symbolic order

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Authors: W. Scott Jackson

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This paper explains the declension of Puritan clerical power following the Great Migration up until when Massachusetts lost its charter in 1684. Historian Perry Miller argued that an overall declension in Puritan culture occurred during this period. However, that notion has been dispelled. There is a resurging field exploring declension in areas outside of Miller’s scope of Puritan culture. I determine that colonial New England existed as a functional theocracy by using Pierre Bourdieu’s theory of symbolic capital to explain clerical power through symbolic and religious misdirection and conversion. I explore civil and economic power struggles in colonial New England during the decades following the Great Migration to establish that Puritan culture did not largely decline. Instead, it was the Puritan clergy’s power that waned during this period.

Keywords: Bourdieu, Historical Sociology, Symbolic Capital, Puritan

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Authors: R. Henry, J-B. Paulin, St. Fauchille, Ph. Delord, K. Benkirane, A. Brunel

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In this paper, the CVA computation of interest rate swap is presented based on its rating. Rating and probability default given by Moody’s Investors Service are used to calculate our CVA for a specific swap with different maturities. With this computation, the influence of rating variation can be shown on CVA. The application is made to the analysis of Greek CDS variation during the period of Greek crisis between 2008 and 2011. The main point is the determination of correlation between the fluctuation of Greek CDS cumulative value and the variation of swap CVA due to change of rating

Keywords: CDS, computation, CVA, Greek crisis, interest rate swap, maturity, rating, swap

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Authors: Jatindranath Gain, Madhumita DasSarkar, Sudakshina Kundu

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Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. Topological quantum computation is concerned with two-dimensional many body systems that support excitations. Anyons are elementary building block of quantum computations. When anyons tunneling in a double-layer system can transition to an exotic non-Abelian state and produce Fibonacci anyons, which are powerful enough for universal topological quantum computation (TQC).Here the exotic behavior of Fibonacci Superlattice is studied by using analytical transfer matrix methods and hence Fibonacci anyons. This Fibonacci anyons can build a quantum computer which is very emerging and exciting field today’s in Nanophotonics and quantum computation.

Keywords: quantum computing, quasicrystals, Multiple Quantum wells (MQWs), transfer matrix method, fibonacci anyons, quantum hall effect, nanophotonics

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Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará

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Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

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Authors: Shao-Di Feng, Von-Wun Soo

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To generate symbolic music with specific emotions is a challenging task due to symbolic music datasets that have emotion labels are scarce and incomplete. This research aims to generate more refined emotions based on the training datasets that are only labeled with four quadrants in Russel’s 2D emotion model. We focus on the theory of Music Fadernet and map arousal and valence to the low-level attributes, and build a symbolic music generation model by combining transformer and GM-VAE. We adopt an in-attention mechanism for the model and improve it by allowing modulation by conditional information. And we show the music generation model could control the generation of music according to the emotions specified by users in terms of high-level linguistic expression and by manipulating their corresponding low-level musical attributes. Finally, we evaluate the model performance using a pre-trained emotion classifier against a pop piano midi dataset called EMOPIA, and by subjective listening evaluation, we demonstrate that the model could generate music with more refined emotions correctly.

Keywords: music generation, music emotion controlling, deep learning, semi-supervised learning

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Authors: Simone Tamires Vieira

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This paper aims to investigate the history of women's schooling in Brazil and to reflect on the condition and social space of women today. Therefore, the following question arises as a research problem: how does the history of the school in/exclusion of women in Brazil relate to the occupations occupied today? As for the objectives, we seek to collect data on the education of women and girls in Brazil, analyze some institutionalized educational legislation and policies, reflect on issues of opportunity and deprivation in order to problematize the female condition through the review of qualitative literature. The results showed that gender and symbolic violence are powerful categories to analyze this theme since the trajectories, choices, and opportunities given to women are permeated by veiled mechanisms perpetuated by a structurally patriarchal society, focused on the interests of the elite, which denies diversity to maintain its status. The aim of this research is to contribute to reflections on the potential of dialogical action, as it highlights the forces that act and permeate the trajectories of women to empower current and future generations.

Keywords: gender, school in/exclusion symbolic violence, women, symbolic violence, women

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Authors: Felipe Aguirre

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In this paper some of the relevant features of the πλῆκτρον within GrecoLatin tradition will be analyzed. Starting from the formal aspects (shape, materials, technical properties) and the archaeological evidence, some of its symbolic implications that emerge in the light of literary and iconographic analysis will be discussed. I shall expose that, in addition to fulfilling a purely physical function within the process of sound production, the πλῆκτρον was the object of a rich imaginery that provided it with an allegorical, metaphorical-poetic and even metaphysical dimension.

Keywords: musicology, ethnomusicology, ancient greek music, plectrum, stringed instruments

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Authors: Rafooneh Mokhtarshahi Sani

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This study explores how the residents of a conserved urban area have used goods and ideas as resources to maintain an enviable architectural identity. Whereas conserved urban quarters are seen as role model for maintaining architectural identity, the article describes how their residents try to give a contemporary modern image to their homes. It is argued that despite the efforts of authorities and decision makers to keep and preserve the traditional architectural identity in conserved urban areas, people have already moved on and have adjusted their homes with their preferred architectural taste. Being through such conflict of interests, have put the future of architectural identity in such places at risk. The thesis is that, on the one hand, such struggle over a desirable symbolic status in identity formation is taking place, and, on the other, it is continuously widening the gap between the real and ideal identity in the built environment. The study then analytically connects the concept of symbolic status to current identity debates. As an empirical research, this study uses systematic social and physical observation methods to describe and categorize the characteristics of settlements in Walled City of Famagusta, which symbolically represent the modern houses. The Walled City is a cultural heritage site, which most of its urban context has been conserved. Traditional houses in this area demonstrate the identity of North Cyprus architecture. The conserved residential buildings, however, either has been abandoned or went through changes by their users to present the ideal image of contemporary life. In the concluding section, the article discusses the differences between the symbolic status of people and authorities in defining a culturally valuable contemporary home. And raises the question of whether we can talk at all about architectural identity in terms of conserving the traditional style, and how we may do so on the basis of dynamic nature of identity and the necessity of its acceptance by the users.

Keywords: symbolic status, architectural identity, conservation, facades, Famagusta walled city

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Authors: Siti Rodliyah, Andrik Purwasito, Bani Sudardi, Abdullah Wakit

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This study employs sociological-ethnographic basic method and the cultural studies paradigm as the approach in understanding the habitus within the customary marriage of the East Nusa Tenggara society who require belis as a bride-price. The conceptual basis underlying the application of habitus theory and symbolic power in East Nusa Tenggara (NTT) society refers to the Bourdieu’s framework. This study is a result of participatory observation on habitus of a marital system using belis observed by the NTT society as a cognitive structure which connects individuals to the social activities of the customary marriage and makes it unquestionable habits. Knowledge of the social world under the pretext of prosperity for the recipients (family) of a bride-price can be a political instrument for the sustainability of power relations. The ritual-mythical system in the society has never been fully present as a neutral habit. The habitus reflected in the marital relationship among the NTT society enables the men to obtain and exercise their power relations. The sustainability of power relations can be seen from the representation of the social status of a girl and the properties attached to her. This is what gave birth to a symbolic rule, in which the social rules about bride-price or belis eventually will serve the interests of those who occupy a dominant position in the social structure, namely the rich men.

Keywords: belis, habitus, East Nusa Tenggara, marital system, power, symbolic

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Yi-Jing Lee

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Prior to the development of ritual design tool and framework, this paper establishes a systematic review on the studies related to ritual and ritual design across anthropology, consumer culture, marketing, and design. It is found that following symbolic anthropologists, the ethnographic approach was adapted by consumer culture researchers to study modern rituals and marketers to enhance consumption. In the domain of design, although there are already designers aware of the importance of ritualistic dimension of human interaction, there are little frameworks for conceptualizing and developing rituals. The conceptualized framework and developing tools is proposed and suggestions of applying it is made in the end of the paper.

Keywords: ritual, ritual design, service design, symbolic interaction

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Authors: Claude Tadonki

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We address the issues related to the computation of the covariance matrix. This matrix is likely to be ill conditioned following its canonical expression, thus consequently raises serious numerical issues. The underlying linear system, which therefore should be solved by means of iterative approaches, becomes computationally challenging. A huge number of iterations is expected in order to reach an acceptable level of convergence, necessary to meet the required accuracy of the computation. In addition, this linear system needs to be solved at each iteration following the general form of the covariance matrix. Putting all together, its comes that we need to compute as fast as possible the associated matrix-vector product. This is our purpose in the work, where we consider and discuss skillful formulations of the problem, then propose a parallel implementation of the matrix-vector product involved. Numerical and performance oriented discussions are provided based on experimental evaluations.

Keywords: covariance-matrix, multicore, numerical computing, parallel computing

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Authors: Kamel Al-Khaled

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Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

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