Abstract
In this paper, we study a class of nonlinear boundary value problems (BVPs) consisting of a more general class of sequential hybrid fractional differential equations (SHFDEs) together with a class of nonlinear boundary conditions at both end points of the domain. The nonlinear functions involved depend explicitly on the fractional derivatives. We study the necessary conditions required for the unique solution to the suggested BVP under the Caratheodory conditions using the technique of measure of noncompactness and degree theory. We also develop conditions for uniqueness results and also on stability analysis.
Highlights
The existence theory for solutions of boundary value problems (BVPs) of hybrid fractional differential equations and sequential hybrid fractional differential equations (SHFDEs) has attracted the attention of many researchers, we refer to [1–11] and the references therein for the recent development in this particular area of interest
1 Introduction The existence theory for solutions of BVPs of hybrid fractional differential equations and SHFDEs has attracted the attention of many researchers, we refer to [1–11] and the references therein for the recent development in this particular area of interest
The purpose of this paper is to investigate existence results for BVPs involving nonlinear boundary conditions at both end points, that is, we study the following class of three point
Summary
The existence theory for solutions of BVPs of hybrid fractional differential equations and SHFDEs has attracted the attention of many researchers, we refer to [1–11] and the references therein for the recent development in this particular area of interest In most of these studies, BVPs with lower order fractional derivatives together with either constant or linear boundary conditions are considered. In case of head flow problems, there are possibilities to have some source or sink on both sides of the boundary (at x = 0 and x = 1) which may be nonlinear functions and a controller at x = ζ0 (0 < ζ0 < 1) Such situation may have importance in application point of view and in theoretical development. The purpose of this paper is to investigate existence results for BVPs involving nonlinear boundary conditions at both end points, that is, we study the following class of three point
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