Existence results for mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions
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Authors
Bashir Ahmad
- 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.
Sotiris K. Ntouyas
- 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.
- Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece.
Jessada Tariboon
- Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand.
- Centre of Excellence in Mathematics, CHE, Ayutthaya Rd., Bangkok 10400, Thailand.
Abstract
In this paper, we investigate a new class of mixed initial value problems of Hadamard and Riemann-
Liouville fractional integro-differential inclusions. The existence of solutions for convex valued (the upper
semicontinuous) case is established by means of Krasnoselskii's fixed point theorem for multivalued maps
and nonlinear alternative criterion, while the existence result for non-convex valued maps (the Lipschitz
case) relies on a fixed point theorem due to Covitz and Nadler. Illustrative examples are also included.
Share and Cite
ISRP Style
Bashir Ahmad, Sotiris K. Ntouyas, Jessada Tariboon, Existence results for mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 6333--6347
AMA Style
Ahmad Bashir, Ntouyas Sotiris K., Tariboon Jessada, Existence results for mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions. J. Nonlinear Sci. Appl. (2016); 9(12):6333--6347
Chicago/Turabian Style
Ahmad, Bashir, Ntouyas, Sotiris K., Tariboon, Jessada. "Existence results for mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 6333--6347
Keywords
- Fractional differential inclusions
- Hadamard derivative
- Riemann-Liouville derivative
- fixed point theorem.
MSC
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