Results 11 to 20 of about 6,558 (265)

Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations

Complexity, 2020
In this paper, three types of fractional order partial differential equations, including the fractional Cauchy–Riemann equation, fractional acoustic wave equation, and two-dimensional space partial differential equation with time-fractional-order, are ...
Haidong Qu, Zihang She, Xuan Liu
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The G′G-expansion method using modified Riemann–Liouville derivative for some space-time fractional differential equations

Ain Shams Engineering Journal, 2014
In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear ...
Ahmet Bekir, Özkan Güner
doaj   +1 more source

Consistent travelling waves solutions to the non-linear time fractional Klein–Gordon and Sine-Gordon equations through extended tanh-function approach

Journal of Taibah University for Science, 2022
In this study, the extended tanh-function method has been used to find further general travelling wave solutions for space-time fractional nonlinear partial differential equations, namely, the time fractional nonlinear Sine-Gordon equation and Klein ...
Umme Sadiya, Mustafa Inc, Mohammad Asif Arefin, M. Hafiz Uddin   +3 more
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Solution of Fractional Partial Differential Equations Using Fractional Power Series Method [PDF]

International Journal of Differential Equations, 2021
In this paper, we are presenting our work where the noninteger order partial differential equation is studied analytically and numerically using the noninteger power series technique, proposed to solve a noninteger differential equation. We are familiar with a coupled system of the nonlinear partial differential equation (NLPDE). Noninteger derivatives
Asif Iqbal Ali, Muhammad Kalim, Adnan Khan   +2 more
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A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

The Scientific World Journal, 2014
We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations.
Özkan Güner, Adem C. Cevikel
doaj   +1 more source

An Efficient Technique of Fractional-Order Physical Models Involving ρ-Laplace Transform

Mathematics, 2022
In this article, the ρ-Laplace transform is paired with a new iterative method to create a new hybrid methodology known as the new iterative transform method (NITM).
Nehad Ali Shah, Ioannis Dassios, Essam R. El-Zahar, Jae Dong Chung   +3 more
doaj   +1 more source

Converting fractional differential equations into partial differential equations

Thermal Science, 2012
A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
Ji-Huan He, Zheng-Biao Li
openaire   +1 more source

An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics. [PDF]

PLoS ONE, 2014
In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is ...
Jamshad Ahmad, Syed Tauseef Mohyud-Din
doaj   +1 more source

Weak Solutions for Time-Fractional Evolution Equations in Hilbert Spaces

Fractal and Fractional, 2021
Our purpose is to introduce a notion of weak solution for a class of abstract fractional differential equations. We point out that the time fractional derivative occurring in the equations is in the sense of the Caputo derivative.
Paola Loreti, Daniela Sforza
doaj   +1 more source

New Fractional Complex Transform for Conformable Fractional Partial Differential Equations [PDF]

Journal of Applied Mathematics, Statistics and Informatics, 2016
Abstract Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations.
Cenesiz, Y., Kurt, A.
openaire   +4 more sources