Existence of solutions of coupled φ-Hilfer fractional differential systems with integral boundary conditions

Abstract

In order to expand the relevant theory of fractional differential equation systems, a class of coupled φ-Hilfer fractional differential systems with integral boundary conditions was studied. Firstly, the coupled φ-Hilfer fractional differential system with integral boundary conditions was transformed into an integral system. Secondly, the appropriate Banach product space and norm were defined, the appropriate integral operator was constructed, and the existence result of the solution of the coupled φ-Hilfer fractional differential system under the integral boundary condition was given by using the compressed image principle and Kransnoselskii's fixed point theorem, respectively. Finally, examples were given to illustrate the correctness of the conclusions obtained. The results show that the solutions of the coupled φ-Hilfer fractional differential system under the integral boundary condition exist. The existence of solutions of coupled φ-Hilfer fractional differential systems is studied for the first time by using the compressed image principle and Kransnoselskii's fixed point theorem, respectively, and some innovative new results are obtained. In addition, the research conclusion enriches the relevant theories of the theoretical solvability of coupled fractional differential systems, and provides certain theoretical reference value for the further study of fractional order differential equations.

Keywords

• analytic theory; φ-hilfer fractional order derivative; coupling system; the principle of compressed images; kransnoselskii's fixed point theorem; existence of solutions