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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


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Volume 18, Issue 1

Issues

Invariant Subspace Method and Exact Solutions of Certain Nonlinear Time Fractional Partial Differential Equations

Ramajayam Sahadevan / Thangarasu Bakkyaraj
Published Online: 2015-02-10 | DOI: https://doi.org/10.1515/fca-2015-0010

Abstract

We show, using invariant subspace method, how to derive exact solutions to the time fractional Korteweg-de Vries (KdV) equation, potential KdV equation with absorption term, KdV-Burgers equation and a time fractional partial differential equation with quadratic nonlinearity. Also we extend the invariant subspace method to nonlinear time fractional differential-difference equations and derive exact solutions of the time fractional discrete KdV and Toda lattice equations.

MSC 2010: Primary 26A33; Secondary 33E12; 34A08; 34K37; 35R11

Key Words and Phrases: invariant subspace method; Mittag-Leffler function; Kilbas-Saigo function; α-analytic function; α-ordinary point; regular α-singular point

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About the article

Received: 2014-05-06

Published Online: 2015-02-10


Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 1, Pages 146–162, ISSN (Online) 1314-2224, DOI: https://doi.org/10.1515/fca-2015-0010.

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