Some Existence and Stability Criteria to a Generalized FBVP Having Fractional Composite <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>p</a:mi> </a:math>-Laplacian Operator
Shahram Rezapour, Sabri T. M. Thabet, Mohammed M. Matar, Jehad Alzabut, Sina Etemad
Abstract
In this paper, we consider a generalized Caputo boundary value problem of fractional differential equation with composite <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:mi>p</a:mi> </a:math> -Laplacian operator. Boundary value conditions of this problem are of three-point integral type. First, we obtain Green’s function in relation to the proposed fractional boundary value problem and then for establishing the existence and uniqueness results, we use topological degree theory and Banach contraction principle. Further, we consider a stability analysis of Ulam-Hyers and Ulam-Hyers-Rassias type. To examine the validity of theoretical results, we provide an illustrative example.