Fundamental solutions of the general fractional‐order diffusion equations

By Xiao-jun Yang, F. Gao, Yang Ju, Hong-Wei Zhou. Mathematical methods in the applied sciences, 2018

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In this article, the general fractional‐order diffusion equations within the negative Prabhakar kernel are considered for the first time. With the aid of the Laplace transform, the series solutions for the problems with the general Mittag‐Leffler functions are discussed in detail. The obtained results are efficient in the description of the anomalous behaviors of the diffusive process.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/83d58b5b7586459bf603c00bc060a338004aef82