Generalized distributed order diffusion equations with composite time fractional derivative

TL;DR

This paper studies generalized distributed order diffusion equations with composite time fractional derivatives, providing solutions via Fox H-functions, analyzing moments with Mittag-Leffler functions, and exploring anomalous diffusion behaviors.

Contribution

It introduces a comprehensive framework for solving and analyzing distributed order diffusion equations with composite derivatives, extending previous models and solutions.

Findings

Decelerating anomalous subdiffusion observed with two composite derivatives

Solutions expressed as infinite series in Fox H-functions

Generalized models include previously known results as special cases

Abstract

In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in Fox $H$-functions. The fractional and second moments are derived by using Mittag-Leffler functions. We observe decelerating anomalous subdiffusion in case of two composite time fractional derivatives. Generalized uniformly distributed order diffusion equation, as a model for strong anomalous behavior, is analyzed by using Tauberian theorem. Some previously obtained results are special cases of those presented in this paper.