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347486

Finite Integral Involving Incomplete Aleph-functions and Fresnel Integral

Article

Last updated: 05 Jan 2025

Subjects

-

Tags

Special Functions

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.

DOI

10.21608/jfca.2024.258033.1053

Keywords

Incomplete Gamma Function, incomplete Aleph-function, Mellin-Barnes integrals contour, Fresnel integral

Authors

First Name

Dheerandra

Last Name

Sachan

MiddleName

Shanker

Affiliation

Mathematics Department, Asst. Professor, St. Mary's PG College, Vidisha, India

Email

sachan.dheerandra17@gmail.com

City

Vidisha

Orcid

0000-0002-9400-3223

First Name

Balram

Last Name

Rajak

MiddleName

-

Affiliation

St. Mary's PG College, Vidisha (MP)

Email

balramrajak2@gmail.com

City

Vidisha

Orcid

-

First Name

Frederic

Last Name

Ayant

MiddleName

-

Affiliation

College Jean L’herminier, Alleedes Nympheas, 83500 La Seyne-sur-Mer, FRANCE

Email

fredericayant@gmail.com

City

La Seyne-sur-Mer

Orcid

-

Volume

15

Article Issue

2

Related Issue

44334

Issue Date

2024-07-01

Receive Date

2023-12-25

Publish Date

2024-07-01

Page Start

1

Page End

9

Print ISSN

2090-584X

Online ISSN

2090-5858

Link

https://jfca.journals.ekb.eg/article_347486.html

Detail API

https://jfca.journals.ekb.eg/service?article_code=347486

Order

5

Type

Regular research papers

Type Code

2,646

Publication Type

Journal

Publication Title

Journal of Fractional Calculus and Applications

Publication Link

https://jfca.journals.ekb.eg/

MainTitle

Finite Integral Involving Incomplete Aleph-functions and Fresnel Integral

Details

Type

Article

Created At

18 Dec 2024