Time-hybrid heat and wave equations on scattered $n$-dimensional coupled-jumping time scales

Z. Li^a, C. Wang^a, R. P. Agarwal<sup>bc

a</sup> Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
^b Florida Institute of Technology
^c Department of Mathematics, Texas A&M University-Kingsville, TX 78363-8202, Kingsville, TX, USA

Abstract: In this paper, the exponential, hyperbolic, and trigonometric functions on $n$-dimensional coupled-jumping time scales (CJTS for short) are introduced. Based on this, we introduce the Laplace transform on $n$-dimensional CJTS and establish their related properties. Moreover, the homogeneous time-hybrid heat and wave equations are solved on scattered $n$-demensional CJTS using this Laplace transform.

Keywords: coupled-jumping time scales, multivariable calculus, partial dynamic equation, Laplace transform.

UDC: 517.44

MSC: 26E70, 35A08, 44A10

Received: 15.03.2022
Revised: 17.05.2022
Accepted: 20.05.2022

Language: English

DOI: 10.15393/j3.art.2022.11910

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