IJPAM: Volume 109, No. 1 (2016)

ON PERTURBED FRACTIONAL DIFFERENTIAL EQUATIONS
AND INCLUSIONS WITH GENERALIZED
RIEMANN-LIOUVILLE FRACTIONAL
INTEGRAL BOUNDARY CONDITIONS

Bashir Ahmad$^1$, Sotiris K. Ntouyas$^{1,2}$
$^1$Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group
Department of Mathematics
Faculty of Science
King Abdulaziz University
P.O. Box 80203, Jeddah 21589, SAUDI ARABIA
$^2$Department of Mathematics
University of Ioannina
451 10, Ioannina, GREECE
$^2$e-mail: [email protected]


Abstract. In this paper, we present the sufficient criteria for the existence of solutions for perturbed fractional differential equations and inclusions with generalized Riemann-Liouville fractional integral boundary conditions. We make use of a nonlinear alternative, which deals with the sum of completely continuous and contractive single-valued or multi-valued operators, to obtain the desired results.

Received: August 1, 2016

AMS Subject Classification: 34A08, 34A12, 34A60

Key Words and Phrases: Caputo fractional derivative, generalized Riemann-Liouville fractional integral, fractional differential inclusions, existence, fixed point theorems

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DOI: 10.12732/ijpam.v109i1.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 1
Pages: 29 - 48


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