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On some properties of the generalized Mittag-Leffler function
Mumtaz Ahmad Khan1, Shakeel Ahmed
1Department of Applied Mathematics, Faculty of Engineering, Aligarh Muslim University, Aligarh, 202002 India.
Springerplus
|September 12, 2013
Summary
This study explores a generalized Mittag-Leffler function, establishing its properties and connections to other special functions. Key findings include its behavior under various transforms and its relationship with hypergeometric functions and polynomials.
Area of Science:
- Mathematics
- Special Functions
- Fractional Calculus
Background:
- Mittag-Leffler functions are crucial in various scientific fields, particularly in solving fractional differential equations.
- Understanding generalized forms enhances their applicability and theoretical framework.
Purpose of the Study:
- To investigate the properties of a generalized Mittag-Leffler type function.
- To establish relationships between this generalized function and other known special functions and polynomials.
Main Methods:
- Analysis of differentiation and integration properties.
- Application of Euler (Beta) transforms, Laplace transforms, and Whittaker transforms.
- Representation using generalized hypergeometric series.
Main Results:
- Derivation of various properties of the generalized Mittag-Leffler function.
- Establishment of connections with Wright hypergeometric function.
- Demonstration of relationships with Laguerre polynomials.
Conclusions:
- The generalized Mittag-Leffler function exhibits rich properties under various analytical operations.
- The established relationships provide new insights into the interconnections between different special functions.
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