scholarly journals A modified exp-function method for fractional partial differential equations

2021 ◽  
pp. 17-17
Author(s):  
Yi Tian ◽  
Jun Liu
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Rational Function ◽  
Fractional Differential Equations ◽  
Present Method ◽  
Function Method ◽  
Solution Procedure ◽  
Algebraic Equations ◽  
Fractional Partial Differential Equations ◽  
Fractional Differential

This paper proposes a novel exponential rational function method, a modification of the well-known exp-function method, to find exact solutions of the time fractional Cahn-Allen equation and the time fractional Phi-4 equation. The solution procedure is reduced to solve a system of algebraic equations, which is then solved by Wu?s method. The results show that the present method is effective, and can be applied to other fractional differential equations.

scholarly journals Hyperbolic rational solutions to a variety of conformable fractional Boussinesq-Like equations

2019 ◽  
Vol 8 (1) ◽  
pp. 224-230 ◽  
Author(s):  
Hadi Rezazadeh ◽  
M.S. Osman ◽  
Mostafa Eslami ◽  
Mohammad Mirzazadeh ◽  
Qin Zhou ◽  
...  
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Rational Function ◽  
Fractional Differential Equations ◽  
Present Method ◽  
Physical Phenomenon ◽  
Ocean Engineering ◽  
Rational Solutions ◽  
Fractional Differential

Abstract The aim of this paper is to investigate hyperbolic rational solutions of four conformable fractional Boussinesq-like equations using the method of exponential rational function (ERF). The present method is a good scheme, reveal distinct exact solutions and convenient for solving other types of nonlinear conformable fractional differential equations. These solutions are of significant importance in coastal and ocean engineering where the fractional Boussinesq-like equations modeled for some special physical phenomenon.

scholarly journals A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Özkan Güner ◽  
Adem C. Cevikel
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Function Method ◽  
Burgers Equation ◽  
Fractional Partial Differential Equations ◽  
New Exact Solutions ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

scholarly journals Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmet Bekir ◽  
Özkan Güner ◽  
Adem C. Cevikel
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Function Method ◽  
Fractional Derivatives ◽  
Fractional Complex Transform ◽  
Fractional Equations ◽  
New Exact Solutions ◽  
Fractional Differential

The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

scholarly journals Exact solutions of conformable fractional differential equations

2021 ◽  
Vol 22 ◽  
pp. 103916
Author(s):  
Haleh Tajadodi ◽  
Zareen A. Khan ◽  
Ateeq ur Rehman Irshad ◽  
J.F. Gómez-Aguilar ◽  
Aziz Khan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Fractional Differential

scholarly journals A numerical scheme for problems in fractional calculus

2018 ◽  
Vol 20 ◽  
pp. 02001
Author(s):  
M. Razzaghi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Numerical Scheme ◽  
Boundary Value ◽  
Bernoulli Polynomials ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Fractional Differential

In this paper, a new numerical method for solving the fractional differential equations with boundary value problems is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is given. This operator is then utilized to reduce the solution of the boundary value problems for fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

scholarly journals An Integral Operational Matrix of Fractional-Order Chelyshkov Functions and Its Applications

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1755
Author(s):  
M. S. Al-Sharif ◽  
A. I. Ahmed ◽  
M. S. Salim
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Operational Matrix ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Science And Engineering ◽  
Numerical Examples ◽  
Fractional Differential

Fractional differential equations have been applied to model physical and engineering processes in many fields of science and engineering. This paper adopts the fractional-order Chelyshkov functions (FCHFs) for solving the fractional differential equations. The operational matrices of fractional integral and product for FCHFs are derived. These matrices, together with the spectral collocation method, are used to reduce the fractional differential equation into a system of algebraic equations. The error estimation of the presented method is also studied. Furthermore, numerical examples and comparison with existing results are given to demonstrate the accuracy and applicability of the presented method.

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