Abstract

We discuss the existence of solution for a multipoint boundary value problem of fractional differential equation. An existence result is obtained with the use of the coincidence degree theory.

Highlights

  • In this paper, we study the multipoint boundary value problemD0α u t f t, u t, D0α−1u t, D0α−2u t e t, 0 < t < 1, mI03−αu 0 0, D0α−2u 0 βj D0α−2u ξj, u1 αiu ηi, j1i1 where 2 < α ≤ 3, 0 < ξ1 < ξ2 < · · · < ξn < 1, n ≥ 1, 0 < η1 < · · · < ηm < 1, m ≥ 2, αi, βj ∈ R, m m n n αiηiα−1 αiηiα−2 1, βj ξj 0, βj 1, i1International Journal of Differential Equations f : 0, 1 × R3 → R satisfying the Caratheodory conditions, e ∈ L1 0, 1

  • We discuss the existence of solution for a multipoint boundary value problem of fractional differential equation

  • We study the multipoint boundary value problem

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Summary

Introduction

We study the multipoint boundary value problemD0α u t f t, u t , D0α−1u t , D0α−2u t e t , 0 < t < 1, mI03−αu 0 0, D0α−2u 0 βj D0α−2u ξj , u1 αiu ηi , j1i1 where 2 < α ≤ 3, 0 < ξ1 < ξ2 < · · · < ξn < 1, n ≥ 1, 0 < η1 < · · · < ηm < 1, m ≥ 2, αi, βj ∈ R, m m n n αiηiα−1 αiηiα−2 1, βj ξj 0, βj 1, i1International Journal of Differential Equations f : 0, 1 × R3 → R satisfying the Caratheodory conditions, e ∈ L1 0, 1. We discuss the existence of solution for a multipoint boundary value problem of fractional differential equation. There are some papers dealing with the solvability of nonlinear boundary value problems of fractional differential equation, by use of techniques of nonlinear analysis fixed-point theorems, Leray-Schauder theory, etc.

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