Hamza Tabti, Mohammed Belmekki

Multiple Positive Solutions for Fractional Boundary Value Problems with Integral Boundary Conditions

In this paper, we study the existence of two or three positive solutions of a class of boundary value problems of nonlinear fractional differential equations with integral boundary conditions. To state our results, we use the functional-type cone expansion-compression fixed point theorem and the Leggett-Williams fixed point theorem, respectively. In addition, we show the effectiveness of the main result by using some examples.

Mathematics Subject Classification: 26A33, 34B18

Key words and phrases: Fractional differential equation, integral boundary conditions, positive solutions, Green's function, Leggett-Williams fixed point theorem