Hilfer Fractional Quantum Derivative and Boundary Value Problems

Mathematics

Phollakrit Wongsantisuk¹  Sotiris K. Ntouyas²  Jessada Tariboon³  Donny Passary³ 

[1] Department of Electronics Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand;Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece;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;

关键词: quantum calculus;    Hilfer derivative;    existence and uniqueness;   

DOI  :  10.3390/math10060878

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown