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Integral transform methods are widely used to solve the several dynamic equations with initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform is introduced in this article as a new integral transform on a time scale  Open image in new window  to solve a system of dynamic equations. The Sumudu transform on time scale  Open image in new window  has not been presented before. The results in this article not only can be applied on ordinary differential equations when T=ℝOpen image in new window, difference equations when T=ℕ0Open image in new window, but also, can be applied for q-difference equations when T=qℕ0Open image in new window, where qℕ0:={qt:t∈ℕ0 for q>1}Open image in new window or T=qℤ¯:=qℤ∪{0}Open image in new window for q > 1 (which has important applications in quantum theory) and on different types of time scales like T=hℕ0Open image in new window, T=ℕ02Open image in new window and T=TnOpen image in new window the space of the harmonic numbers. Finally, we give some applications to illustrate our main results.

A new integral transform on time scales and its applications