Research Article

On a Generalized Mittag-Leffler Function and Fractional Integrals

Volume: 7 Number: 1 March 31, 2024
EN

On a Generalized Mittag-Leffler Function and Fractional Integrals

Abstract

The object of this paper is to study a generalized Mittag-Leffler function and a modified general class of functions which is reducible to several special functions. convergent conditions of these functions are discussed. Some results pertaining to the generalized Mittag-Leffler function and generating relations involving these functions are derived. Further, fractional integrals involving these functions are achieved. Some illustrative exclusive cases of the results are presented.

Keywords

References

  1. [1] E.W. Barnes, The asymptotic expansion of integral functions defined by Taylor’s series, Philos. Trans. Roy. Soc. London Ser. A Math. Phys. Sci., 206 (1906), 249-297.
  2. [2] E.M. Wright, The asymptotic expansion of integral functions defined by Taylor series, I. Philos. Trans. Roy. Soc. London Ser. A Math. Phys. Sci., 238 (1940), 423-451.
  3. [3] T.R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19 (1971), 7-15.
  4. [4] H.M. Srivastava, An introductory overview of fractional-calculus operators based upon the Fox-Wright and related higher transcendental functions, J. Adv. Engrg. comput., 5(3) (2021), 135-166. $\href{http://dx.doi.org/10.55579/jaec.202153.340}{[\mbox{CrossRef}]}$
  5. [5] V. Kumar, On the generalized Hurwitz-Lerch zeta function and generalized Lambert transform, J. Classical Anal., 17 (1) (2021), 55–67. $\href{http://dx.doi.org/10.7153/jca-2021-17-05}{[\mbox{CrossRef}]} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85132267417&origin=resultslist&sort=plf-f&src=s&sid=81fa61a1532600f63071f79cd12df452&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+the+generalized+Hurwitz-Lerch+zeta+function+and+generalized+Lambert+transform%22%29&sl=67&sessionSearchId=81fa61a1532600f63071f79cd12df452&relpos=0}{[\mbox{Scopus}]} %\href{}{[\mbox{Web of Science}]}$
  6. [6] G.M. Mittag-Leffler, Sur la nouvelle function Ea (x), C. R. Acad. Sci. Paris, 137 (1903), 554-558.
  7. [7] A. Wiman, Uber den Fundamentalsatz in der Teorie der Funktionen Ea (x), Acta. Math., 29 (1905), 191-201.
  8. [8] P. Humbert and R.P. Agarwal, la fonction de Mittag-Leffler et quelques unes de ses generalizations, Bull. Sci. Math., 77(2) (1953), 180-185.

Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Early Pub Date

March 29, 2024

Publication Date

March 31, 2024

Submission Date

October 19, 2023

Acceptance Date

December 27, 2023

Published in Issue

Year 2024 Volume: 7 Number: 1

APA
Kumar, V. (2024). On a Generalized Mittag-Leffler Function and Fractional Integrals. Fundamental Journal of Mathematics and Applications, 7(1), 12-25. https://doi.org/10.33401/fujma.1378534
AMA
1.Kumar V. On a Generalized Mittag-Leffler Function and Fractional Integrals. Fundam. J. Math. Appl. 2024;7(1):12-25. doi:10.33401/fujma.1378534
Chicago
Kumar, Virendra. 2024. “On a Generalized Mittag-Leffler Function and Fractional Integrals”. Fundamental Journal of Mathematics and Applications 7 (1): 12-25. https://doi.org/10.33401/fujma.1378534.
EndNote
Kumar V (March 1, 2024) On a Generalized Mittag-Leffler Function and Fractional Integrals. Fundamental Journal of Mathematics and Applications 7 1 12–25.
IEEE
[1]V. Kumar, “On a Generalized Mittag-Leffler Function and Fractional Integrals”, Fundam. J. Math. Appl., vol. 7, no. 1, pp. 12–25, Mar. 2024, doi: 10.33401/fujma.1378534.
ISNAD
Kumar, Virendra. “On a Generalized Mittag-Leffler Function and Fractional Integrals”. Fundamental Journal of Mathematics and Applications 7/1 (March 1, 2024): 12-25. https://doi.org/10.33401/fujma.1378534.
JAMA
1.Kumar V. On a Generalized Mittag-Leffler Function and Fractional Integrals. Fundam. J. Math. Appl. 2024;7:12–25.
MLA
Kumar, Virendra. “On a Generalized Mittag-Leffler Function and Fractional Integrals”. Fundamental Journal of Mathematics and Applications, vol. 7, no. 1, Mar. 2024, pp. 12-25, doi:10.33401/fujma.1378534.
Vancouver
1.Virendra Kumar. On a Generalized Mittag-Leffler Function and Fractional Integrals. Fundam. J. Math. Appl. 2024 Mar. 1;7(1):12-25. doi:10.33401/fujma.1378534

Cited By

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