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Stability analysis of boundary value problems for Caputo proportional fractional derivative of a function with respect to another function via impulsive Langevin equation. (English) Zbl 1484.34044

Summary: In this paper, we discuss existence and stability results for a new class of impulsive fractional boundary value problems with non-separated boundary conditions containing the Caputo proportional fractional derivative of a function with respect to another function. The uniqueness result is discussed via Banach’s contraction mapping principle, and the existence of solutions is proved by using Schaefer’s fixed point theorem. Furthermore, we utilize the theory of stability for presenting different kinds of Ulam’s stability results of the proposed problem. Finally, an example is also constructed to demonstrate the application of the main results.

MSC:

34A08 Fractional ordinary differential equations
34A37 Ordinary differential equations with impulses
34D20 Stability of solutions to ordinary differential equations
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