scholarly journals A New Computational Approach for Solving Fractional Order Telegraph Equations

2021 ◽  
Vol 13 (3) ◽  
pp. 715-732
Author(s):  
A. Devi ◽  
M. Jakhar
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Computational Approach ◽  
Order Problem ◽  
Adomian Decomposition ◽  
Telegraph Equations ◽  
Derivatives Of

In this work, a modified decomposition method namely Sumudu-Adomian Decomposition Method (SADM) is implemented to find the exact and approximate solutions of fractional order telegraph equations. The derivatives of fractional-order are expressed in terms of caputo operator. Some numerical examples are illustrated to examine the efficiency of the proposed technique. Solutions of fractional order telegraph equations are obtained in the form of a series solution. It is observed that the solutions of fractional order telegraph equations converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested method.

scholarly journals An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 426 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
Muhammad Arif
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Telegraph Equation ◽  
High Rate ◽  
Analytical Technique ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Telegraph Equations

In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

scholarly journals Solution of the space-fractional telegraph equations by using HAM

2015 ◽  
Vol 37 ◽  
pp. 320
Author(s):  
Mehdi Abedi-Varaki ◽  
Shahram Rajabi ◽  
Vahid Ghorbani ◽  
Farzad Hosseinzadeh
Keyword(s):  
Homotopy Analysis Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Space And Time ◽  
Adomian Decomposition ◽  
Homotopy Analysis ◽  
Telegraph Equations

In this study by using the Homotopy Analysis Method (HAM) obtained approximate solutions for the space and time-fractional telegraph equations. In Caputo sense (Yildirim, 2010)these equations considered. Examples are solved and the obtained results show to be more accurate than Adomian Decomposition Method (ADM) and are more efficient and commodious.

HYPERCHAOS IN THE FRACTIONAL-ORDER RÖSSLER SYSTEM WITH LOWEST-ORDER

2009 ◽  
Vol 19 (01) ◽  
pp. 339-347 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Point Of View ◽  
Hyperchaotic System ◽  
Adomian Decomposition ◽  
Rossler System ◽  
Fractional Differential ◽  
Rössler System

This Letter analyzes the hyperchaotic dynamics of the fractional-order Rössler system from a time-domain point of view. The approach exploits the Adomian decomposition method (ADM), which generates series solution of the fractional differential equations. A remarkable finding of the Letter is that hyperchaos occurs in the fractional Rössler system with order as low as 3.12. This represents the lowest order reported in literature for any hyperchaotic system studied so far.

Numerical Solution of Nonlinear Volterra Integro-Differential Equations of Fractional Order by Using Adomian Decomposition Method

2014 ◽  
Vol 635-637 ◽  
pp. 1582-1585
Author(s):  
Li Feng Wang ◽  
Yun Peng Ma ◽  
Yong Qiang Yang
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Fractional Order ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Computational Method ◽  
Numerical Example ◽  
Adomian Decomposition

In this work we present a computational method for for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on Adomian Decom-position Method. Convergence analysis is dependable enough to estimate the maximum absolute truncated error of the Adomian series solution. Numerical example is included to demonstrate the validity and applicability of the method.

scholarly journals A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Yahya T. Abdalla
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

scholarly journals Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

2019 ◽  
Vol 24 (1) ◽  
pp. 7 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Asmaa Al-Enazi ◽  
Bassam Z. Albalawi ◽  
Mona D. Aljoufi
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Surface Brightness ◽  
Milky Way ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Canonical Forms ◽  
Exponential Functions ◽  
Adomian Decomposition ◽  
Delay Differential

The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions. The first solution is provided in the form of a power series which agrees with the solution in the literature, while the second expresses the solution in terms of exponential functions which is viewed as a new solution. A rapid rate of convergence has been achieved and displayed in several graphs. Furthermore, only a few terms of the new approximate solution (expressed in terms of exponential functions) are sufficient to achieve extremely accurate numerical results when compared with a large number of terms of the first solution in the literature. In addition, the residual error using a few terms approaches zero as the delay parameter increases, hence, this confirms the effectiveness of the present approach over the solution in the literature.

scholarly journals Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Randhir Singh ◽  
Gnaneshwar Nelakanti ◽  
Jitendra Kumar
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Integral Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Recursive Scheme ◽  
Urysohn Integral Equations ◽  
Adomian Decomposition

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.

scholarly journals Optimal Parameters for Nonlinear Hirota-Satsuma Coupled KdV System by Using Hybrid Firefly Algorithm with Modified Adomian Decomposition

2020 ◽  
Vol 52 (3) ◽  
pp. 339-352
Author(s):  
Omar Saber Qasim ◽  
Karam Adel Abed ◽  
Ahmed F. Qasim
Keyword(s):  
Exact Solutions ◽  
Hybrid Method ◽  
Decomposition Method ◽  
Firefly Algorithm ◽  
Fitness Function ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Optimal Parameters ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper, several parameters of the non-linear Hirota-Satsuma coupled KdV system were estimated using a hybrid between the Firefly Algorithm (FFA) and the Modified Adomian decomposition method (MADM). It turns out that optimal parameters can significantly improve the solutions when using a suitably selected fitness function for this problem. The results obtained show that the approximate solutions are highly compatible with the exact solutions and that the hybrid method FFA_MADM gives higher efficiency and accuracy compared to the classic MADM method.

scholarly journals SOLUTION OF LOCAL FRACTIONAL GENERALIZED FOKKER–PLANCK EQUATION USING LOCAL FRACTIONAL MOHAND ADOMIAN DECOMPOSITION METHOD

Fractals ◽  
2021 ◽  
Author(s):  
SAAD ALTHOBAITI ◽  
RAVI SHANKER DUBEY ◽  
JYOTI GEETESH PRASAD
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Planck Equation ◽  
Approximate Solutions ◽  
Simple Approach ◽  
Graphical Representations ◽  
Fokker Planck Equation ◽  
Adomian Decomposition ◽  
Computational Work ◽  
Fokker Planck

In this paper, we solve the local fractional generalized Fokker–Planck equation. To solve the problem, local fractional Mohand transform with Adomian decomposition method is introduced due to its simple approach and less computational work. Furthermore, for the applicability of the technique, we illustrate some examples and their exact or approximate solutions with their graphical representations.

Sign in / Sign up

Export Citation Format

Share Document