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Time fractional third-order evolution equation: Symmetry analysis, explicit solutions and conservation laws

[+] Author and Article Information
Dumitru Baleanu

Cankaya University, Department of Mathematics, Öǧretmenler, Cad. 1406530, Ankara/Türkiye; Institute of Space Sciences, Magurele, Bucharest, Romania
dumitru@cankaya.edu.tr

Mustafa Inc

Firat University, Science Faculty, Department of Mathematics, 23119, Elaziǧ/Türkiye
minc@firat.edu.tr

Abdullahi Yusuf

Firat University, Science Faculty, Department of Mathematics, 23119, Elaziǧ/Türkiye; Federal University Dutse, Science Faculty, Department of Mathematics, 7156, Jigawa/Nigeria
yusufabdullahi@fud.edu.ng

Aliyu Isa Aliyu

Firat University, Science Faculty, Department of Mathematics, 23119, Elaziǧ/Türkiye; Federal University Dutse, Science Faculty, Department of Mathematics, 7156, Jigawa/Nigeria
aliyu.isa@fud.edu.ng

1Corresponding author.

ASME doi:10.1115/1.4037765 History: Received May 16, 2017; Revised August 14, 2017

Abstract

In this work, Lie symmetry analysis for the time fractional third-order evolution (TOE) equation with Riemann-Liouville (RL) derivative is analyzed. We transform the time fractional TOE equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. We obtain a kind of an explicit power series solution for the governing equation based on the power series theory. Using Ibragimov's nonlocal conservation method to time fractional partial differential equations, we compute conservation laws (Cls) for the TOE equation. 2-D, 3-D, and contour plots for the explicit power series solution are presented.

Copyright (c) 2017 by ASME
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