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Exp-function method for solving fractional partial differential equations. [PDF]

ScientificWorldJournal, 2013
We extend the Exp‐function method to fractional partial differential equations in the sense of modified Riemann‐Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space‐time fractional Fokas equation and the nonlinear fractional Sharma‐Tasso‐Olver (STO) equation ...
Zheng B.
europepmc   +5 more sources

The modified generalized Kudryashov method for nonlinear space–time fractional partial differential equations of Schrödinger type

Results in Physics, 2023
This paper presents a modified version of the generalized Kudryashov method aimed at obtaining exact solutions for fractional partial differential equations of Schrödinger type.
Fushun Liu, Yuqiang Feng
doaj   +1 more source

A Local Fractional Elzaki Transform Decomposition Method for the Nonlinear System of Local Fractional Partial Differential Equations

Fractal and Fractional, 2022
In this paper, the nonlinear system of local fractional partial differential equations is solved via local fractional Elzaki transform decomposition method.
Halil Anac
doaj   +1 more source

Investigation to analytic solutions of modified conformable time–space fractional mixed partial differential equations

Partial Differential Equations in Applied Mathematics, 2022
In this paper, the invariant subspace method (ISM) is developed to obtain the exact solution of linear and nonlinear time and space fractional mixed partial differential equations involving modified conformable fractional derivative (MCFD). Moreover, the
Chavda Divyesh Vinodbhai, Shruti Dubey
doaj   +1 more source

Fractional Calculus and Time-Fractional Differential Equations: Revisit and Construction of a Theory

Mathematics, 2022
For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of operator theory in fractional Sobolev spaces.
Masahiro Yamamoto
doaj   +1 more source

The solutions of nonlinear fractional partial differential equations by using a novel technique

Open Physics, 2022
In this article, the solutions of higher nonlinear partial differential equations (PDEs) with the Caputo operator are presented. The fractional PDEs are modern tools to model various phenomena more accurately.
Alderremy Aisha Abdullah, Khan Hassan, Khan Qasim, Kumam Poom, Aly Shaban, Ahmad Said, Sitthithakerngkiet Kanokwan   +6 more
doaj   +1 more source

Parameter Estimation for Several Types of Linear Partial Differential Equations Based on Gaussian Processes

Fractal and Fractional, 2022
This paper mainly considers the parameter estimation problem for several types of differential equations controlled by linear operators, which may be partial differential, integro-differential and fractional order operators. Under the idea of data-driven
Wenbo Zhang, Wei Gu
doaj   +1 more source

Large Fractional Linear Type Differential Equations

International Journal of Analysis and Applications, 2023
This paper aims to handle some types of fractional differential equations with a fractional-order values β>1. In particular, we propose a novel analytical solution called an atomic solution for certain fractional linear type differential equations as ...
Ma'mon Abu Hammad, Iqbal Jebril, Roshdi Khalil   +2 more
doaj   +1 more source

Application of the Aboodh Transform for Solving Fractional Delay Differential Equations

Universal Journal of Mathematics and Applications, 2020
In this article, we extend the concept of the Aboodh transform to the solution of partial differential equations of fractional order using Caputo's fractional derivative.
Kacem Belghaba, Mohamed Elarbı Benattıa   +1 more
doaj   +1 more source

A reliable method for the space-time fractional Burgers and time-fractional Cahn-Allen equations via the FRDTM

Advances in Difference Equations, 2017
We propose a new method called the fractional reduced differential transform method (FRDTM) to solve nonlinear fractional partial differential equations such as the space-time fractional Burgers equations and the time-fractional Cahn-Allen equation.
Mahmoud S Rawashdeh
doaj   +1 more source