Multiple Fractional Diffusions via Multivariable H-Function

Abstract

In this paper, we introduce a diffusion and wave equation consisting of multidimensional space Riesz-Feller fractional operators and Caputo time fractional derivative. Imposing certain boundary values, we obtain its solution in terms of multivariable H-function and finally making an appeal to our results, we evaluate various multiple fractional diffusions.

Estimated Solutions of Generalized and Multidimensional Churchill’s Diffusion Problems

“…Recently, multidimensional time diffusion problems are solved as separating in space and time variables by the theory of various authors ( [10], [12], [13], [14]). To solve the equation (3.1) or (3.2) by separation in variables, we impose following initial and boundary conditions:…”

“…On the other hand, the theory and application of fractional differential equations in the diverse field, for example, in the dynamics of sphere immersed in an incompressible viscous fluid, oscillatory process with fractional damping, a study of the tension -deformation relationship of viscoelastic materials, and anomalous diffusion problems have been described in the literature by various researchers ( [7], [8], [11], [14], [15], [16], [18] and others) consisting of the general fractional differential equations along with some operators or functions in the form of matrices. By the interacting multispecies, a system of equations in the matrix form also studied by Chandel and Kumar [4] in the ecosystem.…”