Abstract
The objective of this article is to present the computational 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.
Highlights
In the last decade, considerable interest in fractional differential equations has been stimulated due to their numerous applications in the areas of physics, biology, engineering, and other areas
Several numerical and analytical methods have been developed to study the solutions of nonlinear fractional partial differential equations, for details, refer to the work in [1,2,3,4,5,6]
In recent work many authors have demonstrated the depth of mathematics and related physical issues of advection-dispersion equations
Summary
Considerable interest in fractional differential equations has been stimulated due to their numerous applications in the areas of physics, biology, engineering, and other areas. The objective of this paper is to derive the solution of Cauchy type generalized fractional advection A = f (t) /∃M, τi > 0, i = 1, 2 f (t) ≤ Me τj if t ∈ (−1)j for all real t ≥ 0 the Sumudu transform of function f (t) ∈ A is defined as, S f (t) ; u = F (u) =
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