Maximum principle and its application to multi-index Hadamard fractional diffusion equation

Xueyan Ren,A A El-Deeb,Zhanbing Bai,Guotao Wang

doi:10.1186/s13661-019-01299-y

Abstract

This study establishes some new maximum principle which will help to investigate an IBVP for multi-index Hadamard fractional diffusion equation. With the help of the new maximum principle, this paper ensures that the focused multi-index Hadamard fractional diffusion equation possesses at most one classical solution and that the solution depends continuously on its initial boundary value conditions.

Highlights

As is known, the maximum principle is one of the most effective tools to investigate ordinary differential equations
In [3], Korbol and Luchko generalized the mathematical model of variable-order spacetime fractional diffusion equation to analyze some financial data and considered the option pricing as an application of this model
In [4], the authors established the maximum principle for the multi-term time-space Riesz–Caputo fractional differential equation, uniqueness and continuous dependence of the solution as well as presented a numerical method for the specified equation

Summary

Introduction

The maximum principle is one of the most effective tools to investigate ordinary (partial, evolution, fractional) differential equations. They proved the weak maximum principle and established the uniqueness of solutions to the IBVP with Dirichlet boundary conditions. In [4], the authors established the maximum principle for the multi-term time-space Riesz–Caputo fractional differential equation, uniqueness and continuous dependence of the solution as well as presented a numerical method for the specified equation.

Results

Conclusion