MITTAG-LEFFLER FUNCTION, ITS SPECIFIC CASES
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Abstract
In this article, the Mittag-Leffler function, which plays an important role in fractional analysis and problems of mathematical physics, is studied in detail. The definition of this function, its basic analytical properties, its representation in the form of a series, and its connection with the Laplace transformations are highlighted. Also, one-parameter and two-parameter special cases of the Mittag-Leffler function are analyzed, including the transition to an exponential function and its application in the solution of fractional differential equations. In the course of the research, the role of this function in subdiffusion, anomalous transport processes, and problems with nonlocal boundary conditions is substantiated. The obtained results are important for the development of the theory of fractional differential equations and their application in practical problems.
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References
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