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 (FPDEs), we compute conservation laws (CLs) for the TOE equation. Two dimensional (2D), three-dimensional (3D), and contour plots for the explicit power series solution are presented.
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February 2018
Research-Article
Time Fractional Third-Order Evolution Equation: Symmetry Analysis, Explicit Solutions, and Conservation Laws
Dumitru Baleanu,
Dumitru Baleanu
Department of Mathematics,
Cankaya University,
Öčretmenler Cad., 1406530,
Ankara 6400, Turkey;
Institute of Space Sciences,
Magurele, Bucharest 77125, Romania
e-mail: dumitru@cankaya.edu.tr
Cankaya University,
Öčretmenler Cad., 1406530,
Ankara 6400, Turkey;
Institute of Space Sciences,
Magurele, Bucharest 77125, Romania
e-mail: dumitru@cankaya.edu.tr
Search for other works by this author on:
Abdullahi Yusuf,
Abdullahi Yusuf
Department of Mathematics,
Firat University,
Elazič 23119, Turkey;
Department of Mathematics,
Federal University Dutse,
Jigawa 7156, Nigeria
e-mail: yusufabdullahi@fud.edu.ng
Firat University,
Elazič 23119, Turkey;
Department of Mathematics,
Federal University Dutse,
Jigawa 7156, Nigeria
e-mail: yusufabdullahi@fud.edu.ng
Search for other works by this author on:
Aliyu Isa Aliyu
Aliyu Isa Aliyu
Department of Mathematics,
Firat University,
Elazič 23119, Turkey;
Department of Mathematics,
Federal University Dutse,
Jigawa 7156, Nigeria
e-mail: aliyu.isa@fud.edu.ng
Firat University,
Elazič 23119, Turkey;
Department of Mathematics,
Federal University Dutse,
Jigawa 7156, Nigeria
e-mail: aliyu.isa@fud.edu.ng
Search for other works by this author on:
Dumitru Baleanu
Department of Mathematics,
Cankaya University,
Öčretmenler Cad., 1406530,
Ankara 6400, Turkey;
Institute of Space Sciences,
Magurele, Bucharest 77125, Romania
e-mail: dumitru@cankaya.edu.tr
Cankaya University,
Öčretmenler Cad., 1406530,
Ankara 6400, Turkey;
Institute of Space Sciences,
Magurele, Bucharest 77125, Romania
e-mail: dumitru@cankaya.edu.tr
Mustafa Inc
Abdullahi Yusuf
Department of Mathematics,
Firat University,
Elazič 23119, Turkey;
Department of Mathematics,
Federal University Dutse,
Jigawa 7156, Nigeria
e-mail: yusufabdullahi@fud.edu.ng
Firat University,
Elazič 23119, Turkey;
Department of Mathematics,
Federal University Dutse,
Jigawa 7156, Nigeria
e-mail: yusufabdullahi@fud.edu.ng
Aliyu Isa Aliyu
Department of Mathematics,
Firat University,
Elazič 23119, Turkey;
Department of Mathematics,
Federal University Dutse,
Jigawa 7156, Nigeria
e-mail: aliyu.isa@fud.edu.ng
Firat University,
Elazič 23119, Turkey;
Department of Mathematics,
Federal University Dutse,
Jigawa 7156, Nigeria
e-mail: aliyu.isa@fud.edu.ng
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 16, 2017; final manuscript received August 14, 2017; published online November 20, 2017. Assoc. Editor: Zaihua Wang.
J. Comput. Nonlinear Dynam. Feb 2018, 13(2): 021011 (8 pages)
Published Online: November 20, 2017
Article history
Received:
May 16, 2017
Revised:
August 14, 2017
Citation
Baleanu, D., Inc, M., Yusuf, A., and Aliyu, A. I. (November 20, 2017). "Time Fractional Third-Order Evolution Equation: Symmetry Analysis, Explicit Solutions, and Conservation Laws." ASME. J. Comput. Nonlinear Dynam. February 2018; 13(2): 021011. https://doi.org/10.1115/1.4037765
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