A coupled fixed point theorem and application to fractional hybrid differential problems

Abstract

This paper is devoted to the study of the existence of solution to the following system of fractional hybrid differential equations:where D α is the R-L fractional derivative of order α, J = [0, T], T > 0, and the functionsThe proof of the existence theorem is based on a coupled fixed point theorem of Krasnoselskii type, which extends a fixed point theorem of Burton (Appl. Math. Lett. 11:85-88, 1998). Finally, our results are illustrated by a concrete example.

On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions

“…. Besides from the aforesaid problems, recently by using fixed point theory, several remarkable problems have been investigated in FDEs with various boundary conditions, for detail see [2,7,28] and the references therein. Sometimes in many applications like numerical analysis, optimization, mathematical biology, business mathematics, economics etc., we come across the situation where finding the exact solution is quite difficult task.…”

On coupled system of nonlinear hybrid differential equation with arbitrary order

“…For further detailed study, we refer to [1,3,4,28]. Let We need some precise definitions of the basic concepts.…”

Study of Nonlocal Boundary Value Problems of Non-Integer Order Hybrid Differential Equations

“…Recently, a researcher established enough conditions for existence of solutions to the following coupled system of initial value problem for hybrid differential equations of noninteger order (Bashiri et al, 2016). …”