Analytic solution of generalized space time advection-dispersion equation with fractional Laplace operator

Abstract

The aim of this paper is to investigate the solutions of Time-space fractional advection-dispersion equation with Hilfer composite fractional derivative and the space fractional Laplacian operator. The solution of the equation is obtained by applying the Laplace and Fourier transforms, in terms of Mittag-leffler function. The work by R. K. Saxena

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

“…(III). On giving suitable value to the parameters involved in Theorem 3.1, we can obtained same results, earlier given by Haung and Liu [14], Haubold et al [15], Saxena et al [16], and Agarwal et al [17].…”

“…The objective of this paper is to derive the solution of Cauchy type generalized fractional advection dispersion equation (18), associated with the Hilfer-Prabhakar fractional derivative. This paper provides an elegant extension of results, given earlier by Haung and Liu [14], Haubold et al [15], Saxena et al [16], and Agarwal et al [17].…”

A Remark on the Fractional Integral Operators and the Image Formulas of Generalized Lommel–Wright Function

“…Fractional calculus (FC) represents a complex physical phenomenon in a more accurate and efficient way than classical calculus. In recent years, many researchers [1][2][3][4][5][6][7] have used fractional order integral models in real-world problems in various fields of science and technology. There exists several definitions of fractional order integrals in the literature that can be used to solve the fractional integral equations involving special functions.…”

On Hilfer-Prabhakar derivatives Formable integral transform and its applications to fractional differential equations

“…is given by [30] Proof. Applying the Fourier and Formable transforms on equation (4.1) by using the equations (3.3), (2.13).…”

“…where ∆ λ 2 is the fractional generalized Laplace operator of order λ, λ ∈ (0, 2), ρ ∈ (0, 1), ν ∈ [0, 1] : x ∈ R, t ∈ R + , γ > 0 Fourier transform of ∆ λ 2 is −|k| λ discussed in [30] Proof. Applying the Fourier and Formable integral transforms on equation (4.7) by using the equations (3.4), (2.13), first we will aply the Fourier transform…”