TIME-HYBRID HEAT AND WAVE EQUATIONS ON SCATTERED 𝑁-DIMENSIONAL COUPLED-JUMPING TIME SCALES

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