A new approach for solving fractional partial differential equations in the sense of the modified Riemann-Liouville derivative
type: Item
instance of: scholarly article
title: A new approach for solving fractional partial differential equations in the sense of the modified Riemann-Liouville derivative
zbMATH Open document ID: 1407.35054
DOI: 10.1155/2014/307371
author: Bin Zheng
author: Qing-Hua Feng
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: Based on a fractional complex transformation, certain fractional partial differential equation in the sense of the modified Riemann-Liouville derivative is converted into another ordinary differential equation of integer order, and the exact solutions of the latter are assumed to be expressed in a polynomial in Jacobi elliptic functions including the Jacobi sine function, the Jacobi cosine function, and the Jacobi elliptic function of the third kind. The degree of the polynomial can be determined by the homogeneous balance principle. With the aid of mathematical software, a series of exact solutions for the fractional partial differential equation can be found. For demonstrating the validity of this approach, we apply it to solve the space fractional KdV equation and the space-time fractional Fokas equation. As a result, some Jacobi elliptic functions solutions for the two equations are obtained.
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 7016129
Wikidata QID: Q59065690
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/307371
OpenAlex ID: W2110754056
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description: scientific article; zbMATH DE number 7016129