This is an expository article that describes, in brief, one of the preeminent branch of applicable mathematics, roots of which lie in the nucleus of pure mathematics that ruled the research since past six decades. In writing this article though several important research papers were excised yet attempt is made to retain the beauty of fractional calculus. This article, accommodates Stieltjes transform and fractional integral operator on spaces of generalized functions, distributional Laplace-Hankel transform by fractional integral operators, and wavelet transform of fractional integrals for the integral Boehmians.
"Marvels of fractional calculus." Tbilisi Math. J. 10 (1) 295 - 314, Jan 2017. https://doi.org/10.1515/tmj-2017-0019