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The existence aspects along with the stability of solutions to a Hadamard variable order fractional boundary value problem are investigated in this research study. Our results are obtained via generalized intervals and piecewise constant functions and the relevant Green function, by converting the existing Hadamard variable order fractional boundary value problem to an equivalent standard Hadamard fractional boundary problem of the fractional constant order. Further, Darbo’s fixed point criterion along with Kuratowski’s measure of noncompactness is used in this direction. As well as, the Ulam-Hyers-Rassias stability of the proposed Hadamard variable order fractional boundary value problem is established. A numerical example is presented to express our results’ validity.

Darbo Fixed Point Criterion on Solutions of a Hadamard Nonlinear Variable Order Problem and Ulam-Hyers-Rassias Stability