Marvels of fractional calculus. (English) Zbl 1364.26008
Summary: 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.
MSC:
| 26A33 | Fractional derivatives and integrals |
| 44A10 | Laplace transform |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 46F10 | Operations with distributions and generalized functions |
| 46F99 | Distributions, generalized functions, distribution spaces |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 65T60 | Numerical methods for wavelets |
Keywords:
fractional calculus; Laplace-Hankel transform; Stieltjes transform; wavelet transform; distribution spaces; BoehmiansReferences:
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