New criteria for blow up of fractional differential equations

Abstract

In this paper, some new blow-up criteria are given for a single equation, and the blow up problem of the solution of a single nonlocal equation is solved by changing the equation into a system of equations by introducing an auxiliary function. In addition, the theory of ordinary differential equation is extended to partial differential equation by using the first eigenvalue theory. The results show that the blow-up criteria of Caputo and Caputo-Hadamard fractional differential equations are different.