Abstract
This paper deals with existence and uniqueness of solutions to a class of impulsive boundary value problem for nonlinear implicit fractional differential equations involving the Caputo-exponential fractional derivative. The existence results are based on Schaefer’s fixed point theorem and the uniqueness result is established via Banach’s contraction principle. Two examples are given to illustrate the main results.
Highlights
The fractional calculus is a generalization of ordinary differentiation and integration to arbitrary non-integer orders
Fractional differential equations arise in various fields of science and engineering
For some fundamental results on the theory of fractional calculus and fractional ordinary and partial differential equations, we refer to the reader to the books [1, 2, 21, 25, 35], the articles [5, 6, 17], and the references therein
Summary
The fractional calculus is a generalization of ordinary differentiation and integration to arbitrary non-integer orders. Boundary value problems for fractional differential equations have received considerable attention because they occur in the mathematical modeling of a variety of physical processes; see for example [6, 7, 11, 12, 34]. In [27, 31] the authors introduce the exponential fractional calculus and give some existence and uniqueness results for solutions of initial and boundary value problems for fractional differential equations involving Caputo-exponential fractional derivatives (as defined ). The main goal of this paper is to study existence and uniqueness results for solutions to a more general class of impulsive boundary value problem (BVP for short) given by the following nonlinear implicit fractional-order differential equation:. We give two examples to illustrate the applicability of our main results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
