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Existence Theorems for Mixed Riemann–Liouville and Caputo Fractional Differential Equations and Inclusions with Nonlocal Fractional Integro-Differential Boundary Conditions

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Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
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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
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(2), 21; https://doi.org/10.3390/fractalfract3020021
Received: 15 March 2019 / Revised: 11 April 2019 / Accepted: 15 April 2019 / Published: 17 April 2019
In this paper, we discuss the existence and uniqueness of solutions for a new class of single and multi-valued boundary value problems involving both Riemann–Liouville and Caputo fractional derivatives, and nonlocal fractional integro-differential boundary conditions. Our results rely on modern tools of functional analysis. We also demonstrate the application of the obtained results with the aid of examples. View Full-Text
Keywords: fractional derivatives; fractional integral; boundary value problems; existence; uniqueness; fixed-point theorems fractional derivatives; fractional integral; boundary value problems; existence; uniqueness; fixed-point theorems
MDPI and ACS Style

Ntouyas, S.K.; Alsaedi, A.; Ahmad, B. Existence Theorems for Mixed Riemann–Liouville and Caputo Fractional Differential Equations and Inclusions with Nonlocal Fractional Integro-Differential Boundary Conditions. Fractal Fract 2019, 3, 21.

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