Search results for: Ordinary%20differential%20equations

Authors: G.Mehdiyeva, M.Imanova, V.Ibrahimov

Abstract:

Taking into account that many problems of natural sciences and engineering are reduced to solving initial-value problem for ordinary differential equations, beginning from Newton, the scientists investigate approximate solution of ordinary differential equations. There are papers of different authors devoted to the solution of initial value problem for ODE. The Euler-s known method that was developed under the guidance of the famous scientists Adams, Runge and Kutta is the most popular one among these methods. Recently the scientists began to construct the methods preserving some properties of Adams and Runge-Kutta methods and called them hybrid methods. The constructions of such methods are investigated from the middle of the XX century. Here we investigate one generalization of multistep and hybrid methods and on their base we construct specific methods of accuracy order p = 5 and p = 6 for k = 1 ( k is the order of the difference method).

Keywords: Multistep and hybrid methods, initial value problem, degree and stability of hybrid methods

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Authors: Wararit Panichkitkosolkul

Abstract:

The unit root tests based on the robust estimator for the first-order autoregressive process are proposed and compared with the unit root tests based on the ordinary least squares (OLS) estimator. The percentiles of the null distributions of the unit root test are also reported. The empirical probabilities of Type I error and powers of the unit root tests are estimated via Monte Carlo simulation. Simulation results show that all unit root tests can control the probability of Type I error for all situations. The empirical power of the unit root tests based on the robust estimator are higher than the unit root tests based on the OLS estimator.

Keywords: Autoregressive, Ordinary least squares, Type I error, Power of the test, Monte Carlo simulation.

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Authors: Zanariah Abdul Majid, Mohamed Suleiman

Abstract:

The aim of this paper is to investigate the performance of the developed two point block method designed for two processors for solving directly non stiff large systems of higher order ordinary differential equations (ODEs). The method calculates the numerical solution at two points simultaneously and produces two new equally spaced solution values within a block and it is possible to assign the computational tasks at each time step to a single processor. The algorithm of the method was developed in C language and the parallel computation was done on a parallel shared memory environment. Numerical results are given to compare the efficiency of the developed method to the sequential timing. For large problems, the parallel implementation produced 1.95 speed-up and 98% efficiency for the two processors.

Keywords: Numerical methods, parallel method, block method, higher order ODEs.

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Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: Operational matrix of differentiation, Similarity transformation, Shifted second kind Chebyshev wavelets, Stefan problem.

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Authors: Kamil Aida-zade, C. Ardil

Abstract:

In this paper, some problem formulations of dynamic object parameters recovery described by non-autonomous system of ordinary differential equations with multipoint unshared edge conditions are investigated. Depending on the number of additional conditions the problem is reduced to an algebraic equations system or to a problem of quadratic programming. With this purpose the paper offers a new scheme of the edge conditions transfer method called by conditions shift. The method permits to get rid from differential links and multipoint unshared initially-edge conditions. The advantage of the proposed approach is concluded by capabilities of reduction of a parametric identification problem to essential simple problems of the solution of an algebraic system or quadratic programming.

Keywords: dynamic objects, ordinary differential equations, multipoint unshared edge conditions, quadratic programming, conditions shift

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Authors: Jamal A. Gledan, Akrm H. Algnin

Abstract:

The Global Positioning System (GPS), satellite-based technology, has been utilized extensively in the last few years in a wide range of Geometrics and Geographic Information Systems’ (GIS) applications. One of the main challenges dealing with GPS-based heights consists of converting them into Mean Sea Level (MSL) heights, which is used in surveys and mapping.

In this research’s work, differences in heights of 50 points, in northern part of Libya has been carried out by using both ordinary leveling (in which Geoid is the reference datum) and GPS techniques (in which Ellipsoid is the reference datum). In addition, this study utilized the EGM2008 model to obtain the undulation values between the ellipsoidal and orthometric heights. From these values of ellipsoidal heights can be obtained from GPS observations to compute the orthomteric heights. This research presents a suitable alternative, from an economical point of view, to substitute the expensive traditional leveling technique, particularly, for topographic mapping.

Keywords: Geoid undulation, GPS, ordinary and geodetic leveling, orthometric height.

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Authors: R. Moosazadeh

Abstract:

Among the Ottomans, dress was one of the means of expression of the society to which an individual was belonged, and as much as the cloth of the dress, its color reflected the individual's class. Those cloths, and the type and color of the dresses that were worn in the court, were forbidden to ordinary people. In addition, whatever the person's position was, his/her clothes were changed according to that special time and position. The clothes that were worn on trips and ceremonies were different from ordinary clothes in everyday life. At the time of the Ottoman Empire and the old Turkey, the miniature forms, and historical manuscripts were an indicator of the time of that day, and each of them is used as a document from the history of that time for today. The method used in this study is descriptive-analytical and the data collection procedure has been done through library. In this article, the cloth, shape and form of the Kaftan is considered. Firstly, a summary of the history and an explanation of this style of dressing and the importance of it at that time are considered. Finally, by the completion of this research, some of the findings of this research are mentioned, such as the distinctive features of this style and the process of updating it to use it in the present era.

Keywords: Kaftan, cloth, Ottoman, Turkey.

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Authors: Mohammad Ebrahim Kianifar, Ehsan Ahmadi

Abstract:

Reinforced concrete structures experience local defects such as cracks over their lifetime under various environmental loadings. Consequently, they are repaired by mortars to avoid detrimental effects such as corrosion of reinforcement, which in long-term may lead to strength loss of a member or collapse of structures. However, repaired structures may need multiple repairs due to changes in load distribution, and thus, lack of compatibility between mortar and substrate concrete. On the other hand, waste tire rubber alkali-activated (WTRAA)-based materials have very high potential to be used as repair mortars because of their ductility and flexibility, which may delay failure of repair mortar, and thus, provide sufficient compatibility. Hence, this work presents a study on suitability of WTRAA-based materials as mortars for repair of concrete structures through an experimental program. To this end, WTRAA mortars with 15% aggregate replacement, alkali-activated (AA) mortars, and ordinary mortars are made to repair a number of concrete beams. The WTRAA mortars are composed of slag as base material, sodium hydroxide as alkaline activator, and different gradation of waste tire rubber (fine and coarse gradations). Flexural tests are conducted on the concrete beams repaired by the ordinary, AA, and WTRAA mortars. It is found that, despite having lower compressive strength and modulus of elasticity, the WTRAA and AA mortars increase flexural strength of the repaired beams, give compatible failures, and provide sufficient mortar-concrete interface bondings. The ordinary mortars, however, show incompatible failure modes. This study demonstrates promising application of WTRAA mortars in practical repairs of concrete structures.

Keywords: Alkali-activated mortars, concrete repair, mortar compatibility flexural strength, waste tire rubber.

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Authors: G. Revathi, P. Saikrishnan

Abstract:

An analysis is performed to study the influence of nonuniform double slot suction on a steady laminar boundary layer flow over a rotating sphere when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Nonsimilar solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme in combination with the quasi-linearization technique and an appropriate selection of the finer step sizes along the stream-wise direction. The present investigation shows that the point of ordinary separation can be delayed by nonuniform double slot suction if the mass transfer rate is increased and also if the slots are positioned further downstream. In addition, the investigation reveals that double slot suction is found to be more effective compared to a single slot suction in delaying ordinary separation. As rotation parameter increase the point of separation moves upstream direction.

Keywords: Boundary layer, suction, mass transfer, rotating sphere.

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Authors: Kourosh Parand, Zahra Delafkar, Fatemeh Baharifard

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The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.

Keywords: Tau method, semi-infinite, nonlinear ODE, rational Chebyshev, porous media.

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Authors: B. R. Madushan, S. B. Navaratne, I. Wickramasinghe

Abstract:

Toddy sediment (TS) was cultured in a PDA medium to determine initial yeast load, and also it was undergone sun, shade, solar, dehumidified cold air (DCA) and hot air oven (at 400, 500 and 60oC) drying with a view to preserve viability of yeast. Thereafter, this study was conducted according to two factor factorial design in order to determine best preservation method. Therein the dried TS from the best drying method was taken and divided into two portions. One portion was mixed with 3: 7 ratio of TS: rice flour and the mixture was divided in to two again. While one portion was kept under in house condition the other was in a refrigerator. Same procedure was followed to the rest portion of TS too but it was at the same ratio of corn flour. All treatments were vacuum packed in triple laminate pouches and the best preservation method was determined in terms of leavening index (LI). The TS obtained from the best preservation method was used to make foods (bread and hopper) and organoleptic properties of it were evaluated against same of ordinary foods using sensory panel with a five point hedonic scale. Results revealed that yeast load or fresh TS was 58×106 CFU/g. The best drying method in preserving viability of yeast was DCA because LI of this treatment (96%) is higher than that of other three treatments. Organoleptic properties of foods prepared from best preservation method are as same as ordinary foods according to Duo trio test.

Keywords: Biological leavening agent, coconut toddy, fermentation, yeast.

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Authors: Hayder Kamil Shanbara, Felicite Ruddock, William Atherton, Nassier A. Nassir

Abstract:

Cold bitumen emulsion mixture (CBEM) offers a series benefits as compared with hot mix asphalt (HMA); these include environmental factors, energy saving, the resolution of logistical challenges that can characterise hot mix, and the potential to reserve funds. However, this mixture has some problems similar to any bituminous mixtures as it has low early strength, long curing time that needed to obtain the maximum performance, high air voids and considered inferior to HMA. Thus, CBEM has been used in limited applications such as lightly trafficked roads, footways and reinstatements. This laboratory study describes the development of CBEM using ordinary Portland cement (OPC) instead of the traditional mineral filler. Stiffness modulus, moisture damage and temperature sensitivity tests were used to evaluate the mechanical properties of the produced mixtures. The study concluded that there is a substantial improvement in the mechanical properties and moisture damage resistance of CBEMs containing OPC. Also, the produced cement modified CBEM shows a considerable lower thermal sensitivity than the conventional CBEM.

Keywords: Cold bitumen emulsion mixture, moisture damage, OPC, stiffness modulus, temperature sensitivity.

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Authors: S. Guettala, B. Mezghiche

Abstract:

In this paper, the effect of addition the dune sand powder (DSP) on development of compressive strength and hydration of cement pastes was investigated as a function of water/binder ratio, was varied, on the one hand, the percentage of DSP and on the other, the fineness of DSP. In order to understand better the pozzolanic effect of dune sand powder in cement pastes, we followed the mixtures hydration (50% Pure Lime + 50% DSP) by X-ray diffraction. These mixtures the pastes present a hydraulic setting which is due to the formation of a C-S-H phase (calcium silicate hydrate). The latter is semi-crystallized. This study is a simplified approach to that of the mixtures (80% ordinary Portland cement + 20% DSP), in which the main reaction is the fixing of the lime coming from the cement hydration in the presence of DSP, to form calcium silicate hydrate semi-crystallized of second generation. The results proved that up to (20% DSP) as Portland cement replacement could be used with a fineness of 4000 cm²/g without affecting adversely the compressive strength. After 28 days, the compressive strength at 5, 10 and 15% DSP is superior to Portland cement, with an optimum effect for a percentage of the order of 5% to 10% irrespective of the w/b ratio and fineness of DSP.

Keywords: Ordinary Portland Cement, Pure Lime, Dune Sand Powder, Compressive Strength, Hydration.

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Authors: Jonathan Palatz Cedeño

Abstract:

The paper will seek to examine the scope and limitations of the process of construction of ordinary and extraordinary migration regulatory tools of the countries of Latin America, due to the Venezuelan diaspora in Ibero-America (2015-2018). The analysis methodology will be based on a systematic presentation of the existing advances in the subject under a qualitative approach, in which the results are detailed. We hold that an important part of the Latin American countries that used to be the emitters of migrants have had to generate, with greater or lesser success both nationally and regionally, ordinary and extraordinary migration regulatory tools to respond to the rapid intensification of the current Venezuelan migratory flows. This fact beyond implementing policies for the reception and integration of this population marks a new moment that represents a huge challenge both for the receiving States and for the young Ibero-American institutional migration system. Therefore, we can say that measures to adopt reception and solidarity policies, despite being supported by organs of the multilateral system such as UNHCR and IOM, are not found as guidelines for national and regional action, at the expense of the reactions of the respective public opinions and the influence of what to do of the neighboring countries in the face of the problem.

Keywords: Venezuela, migration, Migration policies and governance, Venezuelan diaspora.

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Authors: Rabha W. Ibrahim

Abstract:

We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

Keywords: Fractional calculus, fractional differential equation, Lane-Emden equation, Riemann-Liouville fractional operators, Volterra integral equation.

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Authors: Y. Wang, H. Fukuda, A. Ozaki, H. Sato

Abstract:

In this study, we discussed the effects on the thermal comfort of super high-rise residences that how effected by the high thermal capacity structural components. We considered different building orientations, structures, and insulation methods. We used the dynamic simulation software THERB (simulation of the thermal environment of residential buildings). It can estimate the temperature, humidity, sensible temperature, and heating/cooling load for multiple buildings. In the past studies, we examined the impact of air-conditioning loads (hereinafter referred to as AC loads) on the interior structural parts and the AC-usage patterns of super-high-rise residences. Super-high-rise residences have more structural components such as pillars and beams than do ordinary apartment buildings. The skeleton is generally made of concrete and steel, which have high thermal-storage capacities. The thermal-storage capacity of super-high-rise residences is considered to have a larger impact on the AC load and thermal comfort than that of ordinary residences. We show that the AC load of super-high-rise units would be reduced by installing insulation on the surfaces of interior walls that are not usually insulated in Japan.

Keywords: High-rise Residences, AC Load, Thermal Comfort, Thermal Storage, Insulation Patterns

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Authors: Y. J. Zhou, G. Lu

Abstract:

In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: Analytical method, mechanical responses, spherical wave propagation, traumatic brain injury.

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Authors: Moses, G, Osinubi, K. J.

Abstract:

A laboratory study on the influence of compactive effort on expansive black cotton specimens treated with up to 8% ordinary Portland cement (OPC) admixed with up to 8% bagasse ash (BA) by dry weight of soil and compacted using the energies of the standard Proctor (SP), West African Standard (WAS) or “intermediate” and modified Proctor (MP) were undertaken. The expansive black cotton soil was classified as A-7-6 (16) or CL using the American Association of Highway and Transportation Officials (AASHTO) and Unified Soil Classification System (USCS), respectively. The 7day unconfined compressive strength (UCS) values of the natural soil for SP, WAS and MP compactive efforts are 286, 401 and 515kN/m2 respectively, while peak values of 1019, 1328 and 1420kN/m2 recorded at 8% OPC/ 6% BA, 8% OPC/ 2% BA and 6% OPC/ 4% BA treatments, respectively were less than the UCS value of 1710kN/m2 conventionally used as criterion for adequate cement stabilization. The soaked California bearing ratio (CBR) values of the OPC/BA stabilized soil increased with higher energy level from 2, 4 and 10% for the natural soil to Peak values of 55, 18 and 8% were recorded at 8% OPC/4% BA 8% OPC/2% BA and 8% OPC/4% BA, treatments when SP, WAS and MP compactive effort were used, respectively. The durability of specimens was determined by immersion in water. Soils treatment at 8% OPC/ 4% BA blend gave a value of 50% resistance to loss in strength value which is acceptable because of the harsh test condition of 7 days soaking period specimens were subjected instead of the 4 days soaking period that specified a minimum resistance to loss in strength of 80%. Finally An optimal blend of is 8% OPC/ 4% BA is recommended for treatment of expansive black cotton soil for use as a sub-base material.

Keywords: Bagasse ash, California bearing ratio, Compaction, Durability, Ordinary Portland cement, Unconfined compressive strength.

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Authors: Shafiq ur Rehman, Jane-Lisa Coughlan

Abstract:

Mobiles are considered to be the most frequently used electronic items in world after electricity. It is probably the only device that can be used by any gender with no age limits depending on its functionality. This paper present the interactive interface of Mobile and particularly aiming the use of advanced phones which are also called smart phones. With the changes in the trend where users are now moving from ordinary mobiles to the one with touch screens and facilities such as WiFi and internet browsing.

Keywords: interface design, functionality, intelligent system

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Authors: Rudolf Csikja, Janos Toth

Abstract:

Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.

Keywords: blow up, finite escape time, polynomial ODE, singularity, Lotka–Volterra equation, Painleve analysis, Ψ-series, global existence

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Authors: Andrei A. Kolyshkin

Abstract:

In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail.

Keywords: Numerical methods, "Mathematica", e-learning.

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Authors: Mohammad Fuad Mohammad Naser, Faycal Ikhouane

Abstract:

LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.

Keywords: Hysteresis, LuGre model, operator, (strong) consistency.

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Authors: T. Solonchak, S. Pesina

Abstract:

Lexical invariants, being a sort of stereotypes within the frames of ordinary consciousness, are created by the members of a language community as a result of uniform division of reality. The invariant meaning is formed in person’s mind gradually in the course of different actualizations of secondary meanings in various contexts. We understand lexical the invariant as abstract language essence containing a set of semantic components. In one of its configurations it is the basis or all or a number of the meanings making up the semantic structure of the word.

Keywords: Lexical invariant, invariant theories, polysemantic word, cognitive linguistics.

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Authors: M. Ashaque Meah, M. Shah Noor, M Asif Arefin, Md. Fazlul Karim

Abstract:

A numerical technique in a boundary-fitted curvilinear grid model is developed to simulate the extent of inland inundation along the coastal belts of Peninsular Malaysia and Southern Thailand due to 2004 Indian ocean tsunami. Tsunami propagation and run-up are also studied in this paper. The vertically integrated shallow water equations are solved by using the method of lines (MOL). For this purpose the boundary-fitted grids are generated along the coastal and island boundaries and the other open boundaries of the model domain. A transformation is used to the governing equations so that the transformed physical domain is converted into a rectangular one. The MOL technique is applied to the transformed shallow water equations and the boundary conditions so that the equations are converted into ordinary differential equations initial value problem. Finally the 4^th order Runge-Kutta method is used to solve these ordinary differential equations. The moving boundary technique is applied instead of fixed sea side wall or fixed coastal boundary to ensure the movement of the coastal boundary. The extent of intrusion of water and associated tsunami propagation are simulated for the 2004 Indian Ocean tsunami along the west coast of Peninsular Malaysia and southern Thailand. The simulated results are compared with the results obtained from a finite difference model and the data available in the USGS website. All simulations show better approximation than earlier research and also show excellent agreement with the observed data.

Keywords: Open boundary condition, moving boundary condition, boundary-fitted curvilinear grids, far field tsunami, Shallow Water Equations, tsunami source, Indonesian tsunami of 2004.

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Authors: S. Ratna Sulistiyanti, Adhi Susanto, Thomas Sri Widodo, Gede Bayu Suparta

Abstract:

In this paper, an experimentation to enhance the visibility of hot objects in a thermal image acquired with ordinary digital camera is reported, after the applications of lowpass and median filters to suppress the distracting granular noises. The common thresholding and slicing techniques were used on the histogram at different gray levels, followed by a subjective comparative evaluation. The best result came out with the threshold level 115 and the number of slices 3.

Keywords: enhance, thermal image, thresholding and slicingtechniques, granular noise, hot objects.

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Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

In this paper, a tri–neuron network model with time delay is investigated. By using the Bendixson-s criterion for high– dimensional ordinary differential equations and global Hopf bifurcation theory for functional differential equations, sufficient conditions for existence of periodic solutions when the time delay is sufficiently large are established.

Keywords: Delay, global Hopf bifurcation, neural network, periodicsolutions.

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Authors: T. Penchev, D. Karastoyanov

Abstract:

The results from experimental research of deformation by upsetting and die forging of lead specimens wit controlled impact are presented. Laboratory setup for conducting the investigations, which uses cold rocket engine operated with compressed air, is described. The results show that when using controlled impact is achieving greater plastic deformation and consumes less impact energy than at ordinary impact deformation process.

Keywords: Rocket Engine, Forging Hammer, Sticking Impact, Plastic Deformation.

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Authors: Amir Taghavi, kourosh Parand, Hosein Fani

Abstract:

In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

Keywords: Unsteady gas equation, Generalized Laguerre functions, Lagrangian method, Nonlinear ODE.

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Authors: Adil Al-Rammahi

Abstract:

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

Keywords: Differential Equations, Laplace Transformations.

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Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

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In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.

Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.

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