On nonexistence of solutions to some time-space fractional evolution equations with transformed space argument

TL;DR

This paper investigates conditions under which certain time-space fractional evolution equations with transformed space arguments have no nontrivial solutions, using the nonlinear capacity method, and extends the analysis to a system of such equations.

Contribution

It introduces new nonexistence results for fractional evolution equations with transformed space arguments and applies the nonlinear capacity method to systems of equations.

Findings

Nonexistence of nontrivial solutions under specific conditions

Extension of results to a 2x2 system of equations

Use of nonlinear capacity method for analysis

Abstract

Some results on nonexistence of nontrivial solutions to some time and space fractional differential evolution equations with transformed space argument are obtained via the nonlinear capacity method. The analysis is then used for a $2\times 2$ system of equations with transformed space arguments.