Existence and uniqueness of the solution to Caputo-Hadamard differential equations with delay and nonlocal conditions

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Abstract

In this paper, we established the existence conditions for initial value problems involving the Caputo-Hadamard derivative operator with delay and nonlocal conditions. The problems were analyzed for various source functions. In a special case, we obtained a unique solution. These results were derived by combining the concept of the measure of non-compactness with appropriate applications of fixed point theorems. Additionally, we provided illustrative examples to support the theoretical findings.

Keywords

Caputo-Hadamard derivative / fractional differential / fractional equation / measure / noncompactness

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