On Nabla Shehu Transform And Its Applications | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 15, Issue 1, January 2024, Pages 1-13 PDF (244.97 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2024.229466.1029 | ||
| Authors | ||
| Sneha Chhatraband* 1; Tukaram Thange2 | ||
| 1Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad. | ||
| 2Department of Mathematics, Yogeshwari Mahavidyalaya, Ambajogai. | ||
| Abstract | ||
| Integral transforms on time scales are persuasive and versatile mathematical operators that extend the concepts of classical integral transforms and are applied to functions defined on arbitrary time scales. Time scales can involve a combination of continuous, discrete, and some cases of mixed behaviours. Thus, integral transforms on time scales are more comprehensive for the analysis of time-varying phenomenon are therefore essential in fields where such practices are frequent. In this paper, we introduce the nabla Shehu transform, which is a generalization of the nabla Laplace and nabla Sumudu transforms on time scales, and discuss its existence with respect to fundamental properties such as linearity, transform of derivatives, transform of integrals, and convolution theorem. Further, we find the transform of the fractional integral, Riemann-Liouville fractional derivative, Liouville-Caputo fractional derivative, time scale power function, and Mittag-Leffler function and use them to solve fractional dynamic equations involving Riemann-Liouville and Liouville-Caputo type fractional derivatives in subsequent sections. | ||
| Keywords | ||
| Nabla Shehu transforms; Time scales; Fractional dynamic equations | ||
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