Search results for: discrete event system

Authors: Hesham A. Khalek, Shafik S. Khoury, Remon F. Aziz, Mohamed A. Hakam

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Slipforming operation’s linearity is a source of planning complications, and operation is usually subjected to bottlenecks at any point, so careful planning is required in order to achieve success. On the other hand, Discrete-event simulation concepts can be applied to simulate and analyze construction operations and to efficiently support construction scheduling. Nevertheless, preparation of input data for construction simulation is very challenging, time-consuming and human prone-error source. Therefore, to enhance the benefits of using DES in construction scheduling, this study proposes an integrated module to establish a framework for automating the generation of time schedules and decision support for Slipform construction projects, particularly through the project feasibility study phase by using data exchange between project data stored in an Intermediate database, DES and Scheduling software. Using the stored information, proposed system creates construction tasks attribute [e.g. activities durations, material quantities and resources amount], then DES uses all the given information to create a proposal for the construction schedule automatically. This research is considered a demonstration of a flexible Slipform project modeling, rapid scenario-based planning and schedule generation approach that may be of interest to both practitioners and researchers.

Keywords: discrete-event simulation, modeling, construction planning, data exchange, scheduling generation, EZstrobe

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Authors: Manlika Ratchagit

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This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, Lyapunov functional, linear matrix inequalities

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Authors: Manlika Rajchakit

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This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, lyapunov functional, linear matrix inequalities

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Authors: Jason Sheng-Hong Tsai, Faezeh Ebrahimzadeh, Min-Ching Chung, Shu-Mei Guo, Leang-San Shieh, Tzong-Jiy Tsai, Li Wang

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In this paper, we first construct a new state and disturbance estimator using discrete-time proportional plus integral observer to estimate the system state and the unknown external disturbance for the discrete-time system with an input-to-output direct-feedthrough term. Then, the generalized optimal linear quadratic digital tracker design is applied to construct a proportional plus integral observer-based tracker for the system with an unknown external disturbance to have a desired tracking performance. Finally, a numerical simulation is given to demonstrate the effectiveness of the new application of our proposed approach.

Keywords: non-minimum phase system, optimal linear quadratic tracker, proportional plus integral observer, state and disturbance estimator

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Authors: Anam Alam, Rahim Jamaluddin Kanji

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With the rapid growth of event in everywhere, event extraction has now become an important matter to retrieve the information from the unstructured data. One of the challenging problems is to extract the event from it. An event is an observable occurrence of interaction among entities. The paper investigates the effectiveness of event extraction capabilities of three software tools that are Wandora, Nitro and SPSS. We performed standard text mining techniques of these tools on the data sets of (i) Afghan War Diaries (AWD collection), (ii) MUC4 and (iii) WebKB. Information retrieval measures such as precision and recall which are computed under extensive set of experiments for Event Extraction. The experimental study analyzes the difference between events extracted by the software and human. This approach helps to construct an algorithm that will be applied for different machine learning methods.

Keywords: event extraction, Wandora, nitro, SPSS, event analysis, extraction method, AFG, Afghan War Diaries, MUC4, 4 universities, dataset, algorithm, precision, recall, evaluation

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Authors: Assem El-Ansary

Abstract:

This paper illustrates the event-oriented Behavioral Pattern Analysis (BPA) modeling approach using the Healthcare Multi-Agent System. The Event defined in BPA is a real-life conceptual entity that is unrelated to any implementation. The major contributions of this research are: The Behavioral Pattern Analysis (BPA) modeling methodology. The development of an interactive software tool (DECISION), which is based on a combination of the Analytic Hierarchy Process (AHP) and the ELECTRE Multi-Criteria Decision Making (MCDM) methods.

Keywords: analysis, modeling methodology, software modeling, event-oriented, behavioral pattern, use cases, Healthcare Multi-Agent System

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Authors: S. Fazi, B. Behdani

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The inland transportation of maritime containers entails the use of different modalities whose capacity is typically booked in advance. Containers may miss their scheduled departure time at a terminal for several reasons, such as delays, change of transport modes, multiple bookings pending. In those cases, it may be difficult for transport service providers to find last minute containers to fill the vacant capacity. Similarly to other industries, overbooking could potentially limit these drawbacks at the cost of a lower service level in case of actual excess of capacity in overbooked rides. However, the presence of multiple modalities may provide the required flexibility in rescheduling and limit the dissatisfaction of the shippers in case of containers in overbooking. This flexibility is known with the term 'synchromodality'. In this paper, we evaluate via discrete event simulation the application of overbooking. Results show that in certain conditions overbooking can significantly increase profit and utilization of high-capacity means of transport, such as barges and trains. On the other hand, in case of high penalty costs and limited no-show, overbooking may lead to an excessive use of expensive trucks.

Keywords: discrete event simulation, flexibility, inland shipping, multimodality, overbooking

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Authors: Rafael Iliasov, Alessandro Golkar

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Object detection based on event vision has been a dynamically growing field in computer vision for the last 16 years. In this work, we create multiple channels from a single event camera and propose an event fusion method (EFM) to enhance object detection in event-based vision systems. Each channel uses a different accumulation buffer to collect events from the event camera. We implement YOLOv7 for object detection, followed by a fusion algorithm. Our multichannel approach outperforms single-channel-based object detection by 0.7% in mean Average Precision (mAP) for detection overlapping ground truth with IOU = 0.5.

Keywords: event camera, object detection with multimodal inputs, multichannel fusion, computer vision

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Authors: Emad Alenany, M. Adel El-Baz

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In this paper, the flow of different classes of patients into a hospital is modelled and analyzed by using the queueing network analyzer (QNA) algorithm and discrete event simulation. Input data for QNA are the rate and variability parameters of the arrival and service times in addition to the number of servers in each facility. Patient flows mostly match real flow for a hospital in Egypt. Based on the analysis of the waiting times, two approaches are suggested for improving performance: Separating patients into service groups, and adopting different service policies for sequencing patients through hospital units. The separation of a specific group of patients, with higher performance target, to be served separately from the rest of patients requiring lower performance target, requires the same capacity while improves performance for the selected group of patients with higher target. Besides, it is shown that adopting the shortest processing time and shortest remaining processing time service policies among other tested policies would results in, respectively, 11.47% and 13.75% reduction in average waiting time relative to first come first served policy.

Keywords: queueing network, discrete-event simulation, health applications, SPT

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Authors: Yutae Lee

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This paper considers a discrete-time bulk-arrival bulkservice queueing system, where service capacity varies depending on the previous service time. By using the generating function technique and the supplementary variable method, we compute the distributions of the queue length at an arbitrary slot boundary and a departure time.

Keywords: discrete-time queue, bulk queue, variable service capacity, queue length distribution

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Authors: Smail Tigani, Mohamed Ouzzif

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This work presents a discrete quantitative state prediction algorithm with intelligent behavior making it able to self-improve some performance aspects. The specificity of this algorithm is the capacity of self-rectification of the prediction strategy before the final decision. The auto-rectification mechanism is based on two parallel mathematical models. In one hand, the algorithm predicts the next state based on event transition matrix updated after each observation. In the other hand, the algorithm extracts its residues trend with a linear regression representing historical residues data-points in order to rectify the first decision if needs. For a normal distribution, the interactivity between the two models allows the algorithm to self-optimize its performance and then make better prediction. Designed key performance indicator, computed during a Monte Carlo simulation, shows the advantages of the proposed approach compared with traditional one.

Keywords: discrete state, Markov Chains, linear regression, auto-adaptive systems, decision making, Monte Carlo Simulation

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Authors: Mijoh A. Gbededo, Kapila Liyanage, Ilias Oraifige

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Decision making for sustainable manufacturing design and management requires critical considerations due to the complexity and partly conflicting issues of economic, social and environmental factors. Although there are tools capable of assessing the combination of one or two of the sustainability factors, the frameworks have not adequately integrated all the three factors. Case study and review of existing simulation applications also shows the approach lacks integration of the sustainability factors. In this paper we discussed the development of a simulation based framework for support of a holistic assessment of sustainable manufacturing design and management. To achieve this, a strategic approach is introduced to investigate the strengths and weaknesses of the existing decision supporting tools. Investigation reveals that Discrete Event Simulation (DES) can serve as a rock base for other Life Cycle Analysis frameworks. Simio-DES application optimizes systems for both economic and competitive advantage, Granta CES EduPack and SimaPro collate data for Material Flow Analysis and environmental Life Cycle Assessment, while social and stakeholders’ analysis is supported by Analytical Hierarchy Process, a Multi-Criteria Decision Analysis method. Such a common and integrated framework creates a platform for companies to build a computer simulation model of a real system and assess the impact of alternative solutions before implementing a chosen solution.

Keywords: discrete event simulation, life cycle sustainability analysis, manufacturing, sustainability

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Authors: G. Obregon-Pulido , G. C. Solis-Perales, J. A. Meda-Campaña

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In this paper, we present a sliding mode controller in discrete time. The design of the controller is based on the theory of regulation for nonlinear systems. In the problem of disturbance rejection and/or output tracking, it is known that in discrete time, a controller that uses the zero-order holder only guarantees tracking at the sampling instances but not between instances. It is shown that using the so-called exponential holder, it is possible to guarantee asymptotic zero output tracking error, also between the sampling instant. For stabilizing the problem of close loop system we introduce the sliding mode approach relaxing the requirements of the existence of a linear stabilizing control law.

Keywords: regulation theory, sliding modes, discrete controller, ripple-free tracking

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Authors: Ashish Ashish

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In the last few decades, the discrete chaos of difference equations has gained a massive attention of academicians and scholars due to its tremendous applications in each and every branch of science, such as cryptography, traffic control models, secure communications, weather forecasting, and engineering. In this article, a generalized logistic discrete map is established and discrete chaos is reported through period doubling bifurcation, period three orbit and Lyapunov exponent. It is interesting to see that the generalized logistic map exhibits superior chaos due to the presence of an extra degree of freedom of an ordered parameter. The period doubling bifurcation and Lyapunov exponent are demonstrated for some particular values of parameter and the discrete chaos is determined in the sense of Devaney's definition of chaos theoretically as well as numerically. Moreover, the study discusses an extended chaos based image encryption and decryption scheme in cryptography using this novel system. Surprisingly, a larger key space for coding and more sensitive dependence on initial conditions are examined for encryption and decryption of text messages, images and videos which secure the system strongly from external cyber attacks, coding attacks, statistic attacks and differential attacks.

Keywords: chaos, period-doubling, logistic map, Lyapunov exponent, image encryption

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Authors: Assem El-Ansary

Abstract:

This paper illustrates the event-oriented Behavioral Pattern Analysis (BPA) modeling approach in developing an Intelligent Agent Reservation System (IARS). The Event defined in BPA is a real-life conceptual entity that is unrelated to any implementation. The major contributions of this research are developing the Behavioral Pattern Analysis (BPA) modeling methodology, and developing an interactive software tool (DECISION) which is based on a combination of the Analytic Hierarchy Process (AHP) and the ELECTRE Multi-Criteria Decision Making (MCDM) methods.

Keywords: analysis, intelligent agent, reservation system, modeling methodology, software modeling, event-oriented, behavioral pattern, use cases

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Authors: D. Tedesco, G. Feletti, P. Trucco

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The present study aims to develop a Decision Support System (DSS) to support the operational decision of the Emergency Medical Service (EMS) regarding the assignment of medical emergency requests to Emergency Departments (ED). In the literature, this problem is also known as “hospital selection” and concerns the definition of policies for the selection of the ED to which patients who require further treatment are transported by ambulance. The employed research methodology consists of the first phase of revision of the technical-scientific literature concerning DSSs to support the EMS management and, in particular, the hospital selection decision. From the literature analysis, it emerged that current studies are mainly focused on the EMS phases related to the ambulance service and consider a process that ends when the ambulance is available after completing a request. Therefore, all the ED-related issues are excluded and considered as part of a separate process. Indeed, the most studied hospital selection policy turned out to be proximity, thus allowing to minimize the transport time and release the ambulance in the shortest possible time. The purpose of the present study consists in developing an optimization model for assigning medical emergency requests to the EDs, considering information relating to the subsequent phases of the process, such as the case-mix, the expected service throughput times, and the operational capacity of different EDs in hospitals. To this end, a Discrete Event Simulation (DES) model was created to evaluate different hospital selection policies. Therefore, the next steps of the research consisted of the development of a general simulation architecture, its implementation in the AnyLogic software and its validation on a realistic dataset. The hospital selection policy that produced the best results was the minimization of the Time To Provider (TTP), considered as the time from the beginning of the ambulance journey to the ED at the beginning of the clinical evaluation by the doctor. Finally, two approaches were further compared: a static approach, which is based on a retrospective estimate of the TTP, and a dynamic approach, which is based on a predictive estimate of the TTP determined with a constantly updated Winters model. Findings reveal that considering the minimization of TTP as a hospital selection policy raises several benefits. It allows to significantly reduce service throughput times in the ED with a minimum increase in travel time. Furthermore, an immediate view of the saturation state of the ED is produced and the case-mix present in the ED structures (i.e., the different triage codes) is considered, as different severity codes correspond to different service throughput times. Besides, the use of a predictive approach is certainly more reliable in terms of TTP estimation than a retrospective approach but entails a more difficult application. These considerations can support decision-makers in introducing different hospital selection policies to enhance EMSs performance.

Keywords: discrete event simulation, emergency medical services, forecast model, hospital selection

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Authors: Assem I. El-Ansary

Abstract:

This paper illustrates the event-oriented Behavioral Pattern Analysis (BPA) modeling approach in developing an Multi-Agent Railway Control System (MARCS). The Event defined in BPA is a real-life conceptual entity that is unrelated to any implementation. The major contributions of this research are the Behavioral Pattern Analysis (BPA) modeling methodology, and the development of an interactive software tool (DECISION), which is based on a combination of the Analytic Hierarchy Process (AHP) and the ELECTRE Multi-Criteria Decision Making (MCDM) methods.

Keywords: analysis, multi-agent, railway control, modeling methodology, software modeling, event-oriented, behavioral pattern, use cases

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Authors: S. Channgam, A. Sae-Tang, T. Termsaithong

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In this research, the occurrences of large size events in various system sizes of the Bak-Tang-Wiesenfeld sandpile model are considered. The system sizes (square lattice) of model considered here are 25×25, 50×50, 75×75 and 100×100. The cross-correlation between the ratio of sites containing 3 grain time series and the large size event time series for these 4 system sizes are also analyzed. Moreover, a prediction method of the large-size event for the 50×50 system size is also introduced. Lastly, it can be shown that this prediction method provides a slightly higher efficiency than random predictions.

Keywords: Bak-Tang-Wiesenfeld sandpile model, cross-correlation, avalanches, prediction method

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Authors: Mohamed Hassan Abdullahi

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Decomposition is used as a synthesis tool in several physical systems. It can also be used for tearing and restructuring, which is large-scale system analysis. On the other hand, the commutativity of series-connected systems has fascinated the interest of researchers, and its advantages have been emphasized in the literature. The presentation looks into the necessary conditions for decomposing any third-order discrete-time linear time-varying system into a commutative pair of first- and second-order systems. Additional requirements are derived in the case of nonzero initial conditions. MATLAB simulations are used to verify the findings. The work is unique and is being published for the first time. It is critical from the standpoints of synthesis and/or design. Because many design techniques in engineering systems rely on tearing and reconstruction, this is the process of putting together simple components to create a finished product. Furthermore, it is demonstrated that regarding sensitivity to initial conditions, some combinations may be better than others. The results of this work can be extended for the decomposition of fourth-order discrete-time linear time-varying systems into lower-order commutative pairs, as two second-order commutative subsystems or one first-order and one third-order commutative subsystems.

Keywords: commutativity, decomposition, discrete time-varying systems, systems

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Authors: Ali Cheraghian, Farshid Hajati, Soheila Gheisari, Yongsheng Gao

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In this paper, we present a novel 2.5D face recognition method based on Gabor Discrete Cosine Transform (GDCT). In the proposed method, the Gabor filter is applied to extract feature vectors from the texture and the depth information. Then, Discrete Cosine Transform (DCT) is used for dimensionality and redundancy reduction to improve computational efficiency. The system is combined texture and depth information in the decision level, which presents higher performance compared to methods, which use texture and depth information, separately. The proposed algorithm is examined on publically available Bosphorus database including models with pose variation. The experimental results show that the proposed method has a higher performance compared to the benchmark.

Keywords: Gabor filter, discrete cosine transform, 2.5d face recognition, pose

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Authors: Maja Andrić, Josip Pečarić

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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.

Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality

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Authors: Assem El-Ansary

Abstract:

This paper illustrates the event-oriented Behavioral Pattern Analysis (BPA) modeling approach in developing an Multi-Agent TeleRobotic Security Control System (MTSCS). The event defined in BPA is a real-life conceptual entity that is unrelated to any implementation. The major contributions of this research are the Behavioral Pattern Analysis (BPA) modeling methodology, and the development of an interactive software tool (DECISION), which is based on a combination of the Analytic Hierarchy Process (AHP) and the ELECTRE Multi-Criteria Decision Making (MCDM) methods.

Keywords: analysis, multi-agent, TeleRobotics control, security, modeling methodology, software modeling, event-oriented, behavioral pattern, use cases

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Authors: Duhania O. Mahara, Santi W. Purnami, Aulia N. Fitria, Merissa N. Z. Wirontono, Revina Musfiroh, Shofi Andari, Sagiran Sagiran, Estiana Khoirunnisa, Wahyudi Widada

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For assessing interventions in numerous disease areas, the use of multiple time-to-event outcomes is common. An individual might experience two different events called bivariate time-to-event data, the events may be correlated because it come from the same subject and also influenced by individual characteristics. The bivariate time-to-event case can be applied by copula-based bivariate Cox survival model, using the Clayton and Frank copulas to analyze the dependence structure of each event and also the covariates effect. By applying this method to modeling the recurrent event infection of hemodialysis insertion on chronic kidney disease (CKD) patients, from the AIC and BIC values we find that the Clayton copula model was the best model with Kendall’s Tau is (τ=0,02).

Keywords: bivariate cox, bivariate event, copula function, survival copula

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Authors: Khen Cohen, Daniel Yankelevich, David Mendlovic, Dan Raviv

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We present a 3D stereo system for high-resolution sensing in both the spatial and the temporal domains by combining a frame-based camera and an event-based camera. We establish a method to merge both devices into one unite system and introduce a calibration process, followed by a correspondence technique and interpolation algorithm for 3D reconstruction. We further provide quantitative analysis about our system in terms of depth resolution and additional parameter analysis. We show experimentally how our system performs temporal super-resolution up to effectively 1ms and can detect fast-moving objects and human micro-movements that can be used for micro-expression analysis. We also demonstrate how our method can extract colored events for an event-based camera without any degradation in the spatial resolution, compared to a colored filter array.

Keywords: DVS-CIS stereo vision, micro-movements, temporal super-resolution, 3D reconstruction

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Authors: Hongyu Chen, Li Jiang

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Ubiquitous anomalies endanger the security of our system con- stantly. They may bring irreversible damages to the system and cause leakage of privacy. Thus, it is of vital importance to promptly detect these anomalies. Traditional supervised methods such as Decision Trees and Support Vector Machine (SVM) are used to classify normality and abnormality. However, in some case, the abnormal status are largely rarer than normal status, which leads to decision bias of these methods. Generative adversarial network (GAN) has been proposed to handle the case. With its strong generative ability, it only needs to learn the distribution of normal status, and identify the abnormal status through the gap between it and the learned distribution. Nevertheless, existing GAN-based models are not suitable to process data with discrete values, leading to immense degradation of detection performance. To cope with the discrete features, in this paper, we propose an efficient GAN-based model with specifically-designed loss function. Experiment results show that our model outperforms state-of-the-art models on discrete dataset and remarkably reduce the overhead.

Keywords: GAN, discrete feature, Wasserstein distance, multiple intermediate layers

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Authors: Rogelio Luck, Yucheng Liu

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This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix

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Authors: Alpesh Adeshara, Rajendrasinh Jadeja, Praghnesh Bhatt

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Implementation of advanced technologies requires sophisticated instruments that deal with the operation, control, restoration and protection of rapidly growing power system network under normal and abnormal conditions. Presently, the applications of Phasor Measurement Unit (PMU) are widely found in real time operation, monitoring, controlling and analysis of power system network as it eliminates the various limitations of Supervisory Control and Data Acquisition System (SCADA) conventionally used in power system. The use of PMU data is very rapidly increasing its importance for online and offline analysis. Wide Area Measurement System (WAMS) is developed as new technology by use of multiple PMUs in power system. The present paper proposes a model of MATLAB based PMU using Discrete Fourier Transform (DFT) algorithm and evaluation of its operation under different contingencies. In this paper, PMU based two bus system having WAMS network is presented as a case study.

Keywords: GPS global positioning system, PMU phasor measurement system, WAMS wide area monitoring system, DFT, PDC

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Authors: Ž. Nikolić, H. Smoljanović, N. Živaljić

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This paper presents numerical model based on finite-discrete element method for analysis of the structural response of dry stone masonry structures under static and dynamic loads. More precisely, each discrete stone block is discretized by finite elements. Material non-linearity including fracture and fragmentation of discrete elements as well as cyclic behavior during dynamic load are considered through contact elements which are implemented within a finite element mesh. The application of the model was conducted on several examples of these structures. The performed analysis shows high accuracy of the numerical results in comparison with the experimental ones and demonstrates the potential of the finite-discrete element method for modelling of the response of dry stone masonry structures.

Keywords: dry stone masonry structures, dynamic load, finite-discrete element method, static load

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Authors: Majid Mathlouthi, Fethi Lebdi

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Throughout the world, the extent and magnitude of droughts have economic, social and environmental consequences. Today climate change has become more and more felt; most likely they increase the frequency and duration of droughts. An analysis by event of dry event, from series of observations of the daily rainfall is carried out. A daily precipitation threshold value has been set. A catchment localized in Northern Tunisia where the average rainfall is about 600 mm has been studied. Rainfall events are defined as an uninterrupted series of rainfall days understanding at least a day having received a precipitation superior or equal to a fixed threshold. The dry events are constituted of a series of dry days framed by two successive rainfall events. A rainfall event is a vector of coordinates the duration, the rainfall depth per event and the duration of the dry event. The depth and duration are found to be correlated. So we use conditional probabilities to analyse the depth per event. The negative binomial distribution fits well the dry event. The duration of the rainfall event follows a geometric distribution. The length of the climatically cycle adjusts to the Incomplete Gamma. Results of this analysis was used to study of the effects of climate change on water resources and crops and to calibrate precipitation models with little rainfall records. In response to long droughts in the basin, the drought management system is based on three phases during each of the three phases; different measurements are applied and executed. The first is before drought, preparedness and early warning; the second is drought management, mitigation in the event of drought; and the last subsequent drought, when the drought is over.

Keywords: dry spell, precipitation threshold, climate vulnerability, adaptation measures

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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