Boundary Value Problems for ? -Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions

Surang Sitho, Sotiris K. Ntouyas, Ayub Samadi and Jessada Tariboon
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Surang Sitho: Department of Social and Applied Science, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Ayub Samadi: Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran
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 10800, Thailand

Mathematics, 2021, vol. 9, issue 9, 1-18

Abstract: In the present article, we study a new class of sequential boundary value problems of fractional order differential equations and inclusions involving ? -Hilfer fractional derivatives, supplemented with integral multi-point boundary conditions. The main results are obtained by employing tools from fixed point theory. Thus, in the single-valued case, the existence of a unique solution is proved by using the classical Banach fixed point theorem while an existence result is established via Krasnosel’ski?’s fixed point theorem. The Leray–Schauder nonlinear alternative for multi-valued maps is the basic tool to prove an existence result in the multi-valued case. Finally, our results are well illustrated by numerical examples.

Keywords: fractional differential equations; fractional differential inclusions; Hilfer fractional derivative; Riemann–Liouville fractional derivative; Caputo fractional derivative; boundary value problems; existence and uniqueness; fixed point theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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