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In this paper, we study the existence and uniqueness for a new class of impulsive fractional boundary value problems with separated boundary conditions containing the Caputo fractional derivative of a function with respect to another function. The existence of solutions is established by using the Leray–Schauder nonlinear alternative, and the uniqueness result is proved via Banach’s contraction mapping principle. Some examples are also constructed to demonstrate the application of main results.

Impulsive boundary value problems containing Caputo fractional derivative of a function with respect to another function