ANALYTICAL PROPERTIES OF FRACTIONAL CALCULUS AND TRANSFORMS ASSOCIATED WITH EXTENDED MITTAG-LEFFLER FUNCTION | ||||
| Journal of Fractional Calculus and Applications | ||||
| Volume 16, Issue 2, 2025, Page 1-13 PDF (388.4 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2025.290698.1105 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Nabiullah Khan   ; M. Kamarujjama; Ajija yasmin
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| Department of Applied Mathematics, Aligarh Muslim University, Aligarh | ||||
| Abstract | ||||
| The main object of the present paper is to introduce a new extension of the generalized Mittag-Leffler function utilizing the extended beta function. Among the many properties we evaluated for the extended Mittag - Leffler function are derivative formulas, Mellin transform, Laplace transform, Euler-Beta transform, and Whittaker transform. Further, we establish some results based on the consequences of Riemann-Liouville fractional integral and differential operators on the extended Mittag-Leffler function. The main object of the present paper is to introduce a new extension of the generalized Mittag-Leffler function utilizing the extended beta function. Among the many properties we evaluated for the extended Mittag - Leffler function are derivative formulas, Mellin transform, Laplace transform, Euler-Beta transform, and Whittaker transform. Further, we establish some results based on the consequences of Riemann-Liouville fractional integral and differential operators on the extended Mittag-Leffler function.The main object of the present paper is to introduce a new extension of the generalized Mittag-Leffler function utilizing the extended beta function. Among the many properties we evaluated for the extended Mittag - Leffler function are derivative formulas, Mellin transform, Laplace transform, Euler-Beta transform, and Whittaker transform. Further, we establish some results based on the consequences of Riemann-Liouville fractional integral and differential operators on the extended Mittag-Leffler function. | ||||
| Keywords | ||||
| Extended beta function; generalized Mittag-Leffler function; integral transforms and Riemann-Liouville fractional integrals and derivatives | ||||
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