scholarly journals Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut ◽  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Analytical Solutions ◽  
Order Derivative ◽  
Two Dimensional ◽  
Transform Method ◽  
Sumudu Transform ◽  
Fractional Type

We make use of the so-called Sumudu transform method (STM), a type of ordinary differential equations with both integer and noninteger order derivative. Firstly, we give the properties of STM, and then we directly apply it to fractional type ordinary differential equations, both homogeneous and inhomogeneous ones. We obtain exact solutions of fractional type ordinary differential equations, both homogeneous and inhomogeneous, by using STM. We present some numerical simulations of the obtained solutions and exhibit two-dimensional graphics by means of Mathematica tools. The method used here is highly efficient, powerful, and confidential tool in terms of finding exact solutions.

scholarly journals The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hasan Bulut ◽  
Haci Mehmet Baskonus ◽  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Ordinary Differential Equations ◽  
Fractional Derivatives ◽  
General Setting ◽  
Two Dimensional ◽  
Transform Method ◽  
Symbolic Algebra ◽  
Sumudu Transform

We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM) to some interesting nonhomogeneous fractional ordinary differential equations (FODEs). Finally, we use the solutions to form two-dimensional (2D) graphs, by using the symbolic algebra package Mathematica Program 7.

scholarly journals Discrete Inverse Sumudu Transform Application to Whittaker Equation and Zettl Equation

2018 ◽  
Author(s):  
Rathinavel Silambarasan ◽  
Kottakkaran Sooppy Nisar ◽  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Design Methodology ◽  
Elementary Functions ◽  
New Exact Solutions ◽  
Sumudu Transform ◽  
Sumudu Transforms

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

Numerical solution technique for solving isoperimetric variational problems

2020 ◽  
pp. 2150002
Author(s):  
A. M. S. Mahdy ◽  
E. S. M. Youssef
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Calculus Of Variations ◽  
Variational Problems ◽  
Solution Technique ◽  
Transform Method ◽  
Change Technique ◽  
Main Target ◽  
Sumudu Transform

In this paper, we have a zeal for fulfilling the estimated scientific answers for the calculus of variations by using the Sumudu transform method (STM). The main target is to search the numerical arrangement of ordinary differential equations (ODEs) which emerge from the variational problems where first the fundamental condition for the arrangement of the issue is to fulfill the Euler–Lagrange condition and then solve the equations using STM. The valuable properties of the Sumudu change technique are used to downsize the calculation of the issue to a gathering of straight arithmetical conditions. We introduce four variational problems and discover the numerical solution of those problems using STM and plot the curves of those solutions. These models are picked such that there exist systematic answers for them to offer a reasonable diagram and show the effectiveness of the proposed strategy. Numerical outcomes are registered utilizing Maple programming.

scholarly journals On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Haci Mehmet Baskonus ◽  
Hasan Bulut
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Numerical Results ◽  
Two Dimensional ◽  
Fractional Differential ◽  
Linear And Nonlinear

AbstractIn this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L

scholarly journals Exact Solution of Two-Dimensional Fractional Partial Differential Equations

2020 ◽  
Vol 4 (2) ◽  
pp. 21 ◽  
Author(s):  
Dumitru Baleanu ◽  
Hassan Kamil Jassim
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Sumudu Transform ◽  
Fractional Differential

In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations.

scholarly journals Exact Solutions of the Two-Dimensional Cattaneo Model Using Lie Symmetry Transformations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Khudija Bibi ◽  
Khalil Ahmad
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Lie Symmetry ◽  
Two Dimensional ◽  
Linear Combinations ◽  
Similarity Transformations ◽  
New Exact Solutions ◽  
Symmetry Transformations

In this article, symmetry technique is utilized to obtain new exact solutions of the Cattaneo equation. The infinitesimal symmetries, linear combinations of these symmetries, and corresponding similarity variables are determined, which lead to many exact solutions of the considered equation. By applying similarity transformations, the mentioned partial differential equation is reduced to some ordinary differential equations of second order. Solutions of these ordinary differential equations have yielded many exact solutions of the Cattaneo equation.

scholarly journals On a New Integral Transform and Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
A. Kiliçman ◽  
H. Eltayeb
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Transform ◽  
System Of Differential Equations ◽  
Transform Method ◽  
Control Engineering ◽  
Linear Ordinary Differential Equations ◽  
Sumudu Transform ◽  
Integral Transform Method

Integral transform method is widely used to solve the several differential equations with the initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform was introduced as a new integral transform by Watugala to solve some ordinary differential equations in control engineering. Later, it was proved that Sumudu transform has very special and useful properties. In this paper we study this interesting integral transform and its efficiency in solving the linear ordinary differential equations with constant and nonconstant coefficients as well as system of differential equations.

scholarly journals Fractional Order Airy’s Type Differential Equations of Its Models Using RDTM

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Daba Meshesha Gusu ◽  
Dechasa Wegi ◽  
Girma Gemechu ◽  
Diriba Gemechu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Transform Method ◽  
3 Dimensional

In this paper, we propose a novel reduced differential transform method (RDTM) to compute analytical and semianalytical approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions. The performance of the proposed method was analyzed and compared with a convergent series solution form with easily computable coefficients. The behavior of approximated series solutions at different values of fractional order α and its modeling in 2-dimensional and 3-dimensional spaces are compared with exact solutions using MATLAB graphical method analysis. Moreover, the physical and geometrical interpretations of the computed graphs are given in detail within 2- and 3-dimensional spaces. Accordingly, the obtained approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions exactly fit with exact solutions. Hence, the proposed method reveals reliability, effectiveness, efficiency, and strengthening of computed mathematical results in order to easily solve fractional order Airy’s type differential equations.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

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