On Solutions of Fractional Integrodifferential Systems Involving Ψ-Caputo Derivative and Ψ-Riemann–Liouville Fractional Integral

Abstract

In this paper, we investigate a new class of nonlinear fractional integrodifferential systems that includes the Ψ-Riemann–Liouville fractional integral term. Using the technique of upper and lower solutions, the solvability of the system is examined. We add two examples to demonstrate and validate the main result. The main results highlight crucial contributions to the general theory of fractional differential equations.

Keywords

• Ψ-Caputo derivative
• Ψ-Riemann–Liouville fractional integral
• monotone sequences
• upper and lower solutions
• Arzelà–Ascoli theorem