On inclusion problems involving Caputo and Hadamard fractional derivatives

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Published Dec 12, 2019

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Bashir Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
Sotiris K. Ntouyas
Department of Mathematics, University of Ioannina, Ioannina, Greece; Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
Jessada Tariboon
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand

Abstract

In this paper, we study the existence of solutions to  new inclusion problems  involving both Caputo and Hadamard fractional derivatives, and separated boundary conditions. We apply the modern tools of the fixed point theory to study the  cases when the multi-valued map (the right hand-side of the inclusions) takes convex  as well as non-convex values.  Examples illustrating the abstract results are also presented.

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How to Cite
Ahmad, B., Ntouyas, S., & Tariboon, J. (2019). On inclusion problems involving Caputo and Hadamard fractional derivatives. Acta Mathematica Universitatis Comenianae, 89(1), 169-183. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1071/797
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Vol 89 No 1 (2020): AMUC
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Articles