Hilfer Fractional Quantum Derivative and Boundary Value Problems

Phollakrit Wongsantisuk, Sotiris K. Ntouyas, Donny Passary and Jessada Tariboon
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Phollakrit Wongsantisuk: Department of Electronics Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Donny Passary: 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
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, 2022, vol. 10, issue 6, 1-14

Abstract: In this paper, we introduce an extension of the Hilfer fractional derivative, the “Hilfer fractional quantum derivative”, and establish some of its properties. Then, we introduce and discuss initial and boundary value problems involving the Hilfer fractional quantum derivative. The existence of a unique solution of the considered problems is established via Banach’s contraction mapping principle. Examples illustrating the obtained results are also presented.

Keywords: quantum calculus; Hilfer derivative; existence and uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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