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.
Chhatraband, S., & Thange, T. (2024). On Nabla Shehu Transform And Its Applications. Journal of Fractional Calculus and Applications, 15(1), 1-13. doi: 10.21608/jfca.2024.229466.1029
MLA
Sneha Chhatraband; Tukaram Thange. "On Nabla Shehu Transform And Its Applications". Journal of Fractional Calculus and Applications, 15, 1, 2024, 1-13. doi: 10.21608/jfca.2024.229466.1029
HARVARD
Chhatraband, S., Thange, T. (2024). 'On Nabla Shehu Transform And Its Applications', Journal of Fractional Calculus and Applications, 15(1), pp. 1-13. doi: 10.21608/jfca.2024.229466.1029
VANCOUVER
Chhatraband, S., Thange, T. On Nabla Shehu Transform And Its Applications. Journal of Fractional Calculus and Applications, 2024; 15(1): 1-13. doi: 10.21608/jfca.2024.229466.1029