Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms

• Main Authors: Vinod Gill, Jagdev Singh, Yudhveer Singh
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2019-01-01
• Series: Frontiers in Physics
• Subjects: space-time fractional advection-dispersion equation; Fourier transforms; Sumudu transforms; Hilfer-Prabhakar fractional derivative; fractional laplacian operator; Mittag-Leffler function
• Online Access: https://www.frontiersin.org/article/10.3389/fphy.2018.00151/full

The objective of this article is to present the computable solution of space-time advection-dispersion equation of fractional order associated with Hilfer-Prabhakar fractional derivative operator as well as fractional Laplace operator. The method followed in deriving the solution is that of joint Sumudu and Fourier transforms. The solution is derived in compact and graceful forms in terms of the generalized Mittag-Leffler function, which is suitable for numerical computation. Some illustration and special cases of main theorem are also discussed.