Article
Kyungpook Mathematical Journal 2021; 61(1): 139-153
Published online March 31, 2021
Copyright © Kyungpook Mathematical Journal.
Existence of Positive Solutions for a Class of Conformable Fractional Differential Equations with Parameterized Integral Boundary Conditions
Faouzi Haddouchi
Department of Physics, University of Sciences and Technology of Oran-MB, El Mnaouar, BP 1505, 31000 Oran, Algeria Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, 31000 Oran, Algeria
e-mail : fhaddouchi@gmail.com
Received: June 10, 2019; Revised: June 2, 2020; Accepted: June 2, 2020
In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green's function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.
Keywords: conformable fractional derivatives, integral boundary value problems, positive solutions, fixed point theorems, cone.