### The existence of positive solutions for a Caputo-Hadamard boundary value problem with an integral boundary condition

#### Keywords:

Boundary value problem, Caputo-Hadamard derivative, integral boundary condition, a − θ-Geraghty contraction.#### Abstract

In this research, by entering an a−θ-Geraghty contraction, the existence of a positive solution for a boundary value problem with Caputo-Hadamard derivative including an integral boundary condition is studied. These new results improve and generalize the results stated in the literature. Some examples support and clarify our findings.

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*Advances in the Theory of Nonlinear Analysis and Its Application*,

*7*(5), 155-164. https://doi.org/10.17762/atnaa.v7.i5.332