Generalized fractional calculus on time scales based on the generalized Laplace transform

Xin Li, Weiyuan Ma and Xionggai Bao

Chaos, Solitons & Fractals, 2024, vol. 180, issue C

Abstract: This paper aims to develop definitions and properties about the generalized Laplace transform, fractional integral and derivative on time scales. On the basis of the α−derivative and generalized exponential function, the Laplace transform is extended to the generalized case with respect to another function on time scales. Then, the generalized fractional integral and derivative on time scales are defined by employing the inverse generalized Laplace transform to unify a variety of definitions about continuous and discrete fractional calculus. Moreover, some significant theorems are derived to further increase the availability of these proposed operators. Finally, two examples with different kernel functions are given to verify the feasibility of the theoretical results.

Keywords: Time scales; Generalized Laplace transform; Kernel function; Generalized fractional calculus (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924001504

DOI: 10.1016/j.chaos.2024.114599

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