Existence results for a system of sequential differential equations with varying fractional orders via Hilfer-Hadamard sense

We investigate the criteria for both the existence and uniqueness of solutions within a nonlinear coupled system of Hilfer-Hadamard sequential fractional differential equations featuring varying orders. This system is complemented by nonlocal coupled Hadamard fractional integral boundary conditions. The desired outcomes are attained through the application of well-established fixed-point theorems. It is underscored that the fixed-point approach serves as an effective method for establishing both the existence and uniqueness of solutions to boundary value problems. The results obtained are further demonstrated and validated through illustrative examples.