The Journal of the Indian Mathematical Society

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Solutions of Some Linear Fractional Partial Differential Equations in Mathematical Physics


Affiliations
1 Department of Mathematics, Datta Meghe Institute of Engineering Technology and Research, Wardha, M.S., India
2 Department of Mathematics, Government Science College, Gadchiroli, M.S., India
     

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In this article, we use double Laplace transform method to find solution of general linear fractional partial differential equation in terms of Mittag-Leffler function subject to the initial and boundary conditions. The efficiency of the method is illustrated by considering fractional wave and diffusion equations, Klein-Gordon equation, Burger’s equation, Fokker-Planck equation, KdV equation, and KdV-Burger’s equation of mathematical physics.

Keywords

Double Laplace Transform, Inverse Laplace Transform, Fractional Partial Differential Equation, Caputo Fractional Derivatives.
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  • Solutions of Some Linear Fractional Partial Differential Equations in Mathematical Physics

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Authors

Ranjit R. Dhunde
Department of Mathematics, Datta Meghe Institute of Engineering Technology and Research, Wardha, M.S., India
G. L. Waghmare
Department of Mathematics, Government Science College, Gadchiroli, M.S., India

Abstract


In this article, we use double Laplace transform method to find solution of general linear fractional partial differential equation in terms of Mittag-Leffler function subject to the initial and boundary conditions. The efficiency of the method is illustrated by considering fractional wave and diffusion equations, Klein-Gordon equation, Burger’s equation, Fokker-Planck equation, KdV equation, and KdV-Burger’s equation of mathematical physics.

Keywords


Double Laplace Transform, Inverse Laplace Transform, Fractional Partial Differential Equation, Caputo Fractional Derivatives.

References