AIMS Mathematics, 2019, 4(1): 26-42. doi: 10.3934/Math.2019.1.26

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A study of fractional differential equations and inclusions involving generalized Caputo-type derivative equipped with generalized fractional integral boundary conditions

Bashir Ahmad, Madeaha Alghanmi, Sotiris K. Ntouyas, Ahmed Alsaedi

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

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Special Issues: New trends of numerical and analytical methods with application to real world models for instance RLC with new nonlocal operators

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In this paper, we introduce a new kind of generalized fractional integral boundary conditions and develop the existence theory for a fractional di erential equation involving generalized Caputotype fractional derivative equipped with these conditions. We also study the inclusion case of the given problem. Examples are constructed to demonstrate the application of the obtained results.
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