Finite Integral Involving Incomplete Aleph-functions and Fresnel Integral | ||||
| Journal of Fractional Calculus and Applications | ||||
| Article 5, Volume 15, Issue 2, July 2024, Page 1-9 PDF (341.42 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2024.258033.1053 | ||||
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| Authors | ||||
Dheerandra Shanker Sachan   1; Balram Rajak2; Frederic Ayant3
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| 1Mathematics Department, Asst. Professor, St. Mary's PG College, Vidisha, India | ||||
| 2St. Mary's PG College, Vidisha (MP) | ||||
| 3College Jean L’herminier, Alleedes Nympheas, 83500 La Seyne-sur-Mer, FRANCE | ||||
| Abstract | ||||
| Special functions represent a class of mathematical functions that have achieved a distinct and recognized status within the realms of mathematical analysis, functional analysis, geometry, physics, and diverse practical applications. These functions have emerged as notable tools in these disciplines, owing to their unique properties and inherent significance. Over time, they have become firmly established due to their ability to address specific mathematical challenges and contribute valuable insights to various branches of science and engineering. The primary objective of this paper is to establish a thorough definition of comprehensive finite integrals through the incorporation of both the Fresnel integral and incomplete Aleph-functions. By adopting a unified and general approach, these integrals are shown to yield a diverse range of new outcomes, particularly in specific scenarios. To elucidate and underscore the significance of our contributions, we present a detailed exposition of our findings, accompanied by specific corollaries. These corollaries, in turn, are emphasized as special cases derived directly from the fundamental results outlined in our study. | ||||
| Keywords | ||||
| Incomplete Gamma function; incomplete Aleph-function; Mellin-Barnes integrals contour; Fresnel integral | ||||
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