International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2569

Full Length Research Paper

A nonlocal integral boundary value problem of nonlinear integro-differential equations of fractional order

Bashir Ahmad*, Ahmed Alsaedi and Safa Alsulami
Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Email: [email protected]

  •  Accepted: 08 October 2012
  •  Published: 30 September 2013


This study discussed the existence of solutions for a nonlinear fractional integro-differential equation of order  with four-point nonlocal integral boundary conditions. The given problem is transformed to an equivalent fixed point problem in terms of an operator equation. Then, by means of Banach contraction principle and a fixed point theorem due to Krasnoselskii, the existence results are obtained. The last existence result is based on nonlinear alternative of Leray-Schauder type. An illustrative example is also presented.


Key words: Integro-differential equations, fractional order, four-point integral boundary conditions, fixed point theorems, Leray-Schauder degree.