Abstract
The main objective of the paper is to study the properties of the solution of a certain partial dynamic equation on time scales. The tools employed are based on the application of the Banach fixed-point theorem and a certain integral inequality with explicit estimates on time scales.
Highlights
There has been a lot of interest in shown studying various properties of dynamic equations on time scales by various authors [1–11]
We study some partial dynamic equations on time scales
Let R denote the set of real numbers, Z the set of integers, and T the arbitrary time scales
Summary
There has been a lot of interest in shown studying various properties of dynamic equations on time scales by various authors [1–11]. We study some partial dynamic equations on time scales. Let R denote the set of real numbers, Z the set of integers, and T the arbitrary time scales. Many physical systems can be modeled using dynamical systems on time scales. As response to the needs of diverse applications, many authors have studied qualitative properties of various equations on time scales [4–9, 11]. Motivated by the results in this paper, I consider the partial dynamic equation of the form uΔ2Δ1 (x, y) = f (x, y, u (x, y) , uΔ2Δ1 (x, y) , (Hu) (x, y)) , (1). × Rn × ∫yy[0] g(x, y, m, n, 0, 0)ΔnΔm
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