Solutions of Some Linear Fractional Partial Differential Equations in Mathematical Physics


  • Datta Meghe Institute of Engineering, Technology and Research, Department of Mathematics, Wardha, India
  • Government Science College, Department of Mathematics, Gadchiroli, India


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.


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

Subject Discipline

Mathematical Sciences

Full Text:


L. Debnath and D. Bhatta, Solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics, Fractional Calculus and Applied Analysis, volume 7, number 1, 2004.

Z. Odibat and S. Momani, The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics, Computers and Mathematics with Applications, volume 58, 2199-2208, 2009.

M. Dehghan, J. Manaan, and A. Saadatmandi, The solution of the linear fractional partial differential equations using the homotopy analysis method, Z. Naturforsch., 65a, 935-949, 2010.

A. Anwar, F. Jarad, D. Baleanu and F. Ayaz, Fractional caputo heat equation within the double Laplace transform, Romanian Journal Physics, volume 58, no. 1-2, pp.15-22, 2013.

Ranjit R. Dhunde and G. L. Waghmare, Double Laplace transform method for solving space and time fractional telegraph equations, International Journal of Mathematics and Mathematical sciences, volume 2016, Article ID 1414595, 7 pages, 2016.

S. Momani and Z. Odibat, A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula, Journal of Computational and Applied Mathematics, volume 220, pp. 85-95, 2008.

Ranjit R. Dhunde and G. L. Waghmare, Double Laplace transform method in mathematical physics, International Journal of Theoretical and Mathematical Physics, volume 7, Issue 1, 2017, pp. 14-20.

Ian N. Sneddon, The use of integral transforms, Tata Mcgraw Hill Edition, 1974.

L. Debnath, The double Laplace transforms and their properties with applications to functional, integral and partial differential equations, International Journal of Applied and Computational Mathematics, vol. 2, no. 2, pp. 223-241, 2016.

I. Podlubny, Fractional Differential equations, Academic Press, New York, 1999.

J. Song, F. Yin, X. Cao, and F. Lu, Fractional variational iteration method versus Adomian's decomposition method in some fractional partial differential equations, Journal of Applied Mathematics, volume 2013, Article ID 392567, 10 pages, 2013.

A. A. Elbeleze, A. Kilicman, and B. M. Taib, Fractional Variational Iteration Method and its application to fractional partial differential equation, Mathematical Problems in Engineering, volume 2013, Article ID 543848, 10 pages, 2013.

A. A. Hemeda, Modied homotopy perturbation method for solving fractional differential equations, Journal of Applied Mathematics, volume 2014, Article ID 594245, 9 pages, 2014.

A. S. V. Ravi Kant, and K. Aruna, Solution of fractional third-order dispersive partial differential equations, Egyptian Journal of Basic and Applied Sciences, volume 2, 2015, pp. 190-199.


  • There are currently no refbacks.