SUMUDU TRANSFORM ON TIME SCALES AND ITS APPLICATIONS

Abstract

Abstract. Integral transform method is widely used to solve the sev-eral dynamic di¤erential equations with initial values or boundary conditionswhich are represented by integral equations. With this purpose, the Sumudutransform is introduced in this paper as a new integral transform on a timescale T0 to solve some dynamic di¤erential equations. Sumudu transformon time scale T0 is not presented before. The results in this paper are notonly can be applied on ordinary di¤erential equations when T0 = R, dif-ference equations when T0= N0; but also, can be applied for qô€€€di¤erenceequations when T0=qN0 [ f0g; where qN0 := fqt : t 2 N0 for q > 1g orT0 = qZ := qZ [f0g for q > 1 (which has important applications in quantumtheory) and on di¤erent types of time scales like T0 = hN0, T0 = N20andT0 = f0g [ Tn the space of the harmonic numbers. Finally, we give someapplications to illustrate our main results.