Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (6): 2122-2130.doi: 10.1016/S0252-9602(11)60388-3

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EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

Bashir Ahmad1| Juan J. Nieto1,2| Ahmed Alsaedi1   

  1. 1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;
    2. Departamento de An´alisis Matem´atico, Facultad de Matem´aticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain
  • Received:2011-05-04 Online:2011-11-20 Published:2011-11-20

Abstract:

In this paper, we study a boundary value problem of nonlinear fractional dif-ferential equations of order q (1 < q  2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.

Key words: fractional differential equations, non-separated integral boundary condi-tions, contraction principle, Krasnoselskii´s fixed point theorem, Leray-Schauder degree

CLC Number: 

  • 26A33
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