Investigation of a Coupled System of Hilfer–Hadamard Fractional Differential Equations with Nonlocal Coupled Hadamard Fractional Integral Boundary Conditions

Abstract

We investigate the existence criteria for solutions of a nonlinear coupled system of Hilfer–Hadamard fractional differential equations of different orders complemented with nonlocal coupled Hadamard fractional integral boundary conditions. The desired results are accomplished with the aid of standard fixed-point theorems. We emphasize that the fixed point approach is one of the effective methods to establish the existence results for boundary value problems. Examples illustrating the obtained results are constructed.

Keywords

• Hadamard fractional derivative
• Hilfer–Hadamard fractional derivative
• nonlocal integral boundary conditions
• existence and uniqueness
• fixed point