SOME APPLICATIONS OF FRACTIONAL DERIVATIVE AND MITTAG-LEFFLER FUNCTION | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 15, Issue 2, July 2024, Pages 1-14 PDF (260.95 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2024.275299.1075 | ||
| Author | ||
| Arun digras* | ||
| Department of Mathematics, Government Polytechnic, Hingoli - 431 513, Maharashtra, India | ||
| Abstract | ||
| There are different approaches to the fractional calculus which, not being all equivalent, have lead to a certain degree of confusion and several misunderstandings in the literature. Probably for this the fractional calculus is in some way the ”black sheep” of the analysis. In spite of the numerous eminent mathematicians who have worked on it, still now the fractional calculus is object of so many prejudices. In these review lectures we essentially consider and develop two different approaches to the fractional calculus in the framework of the real analysis: the continuous one, based integral operators and the discrete one, based on infinite series of finite differences with increments tendig to zero. Both approaches turn out to be useful in treating our generalized diffusion processes in the theory of probability and stochastic processes.We obtain basic properties like coefficient inequality, distortion and covering theorem, radii of starlikeness, convexity and closeto-convexity, extreme points, Hadamard product, and closure theorems for functions belonging to our class | ||
| Keywords | ||
| Univalent; derivative opertator; Starlike; Extreme points; Hadamard product | ||
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