MITTAG-LEFLER FUNCTION AND ITS ASYMPTOTICS

Authors

  • Sapayev Oybek Azadboy ugli 1st-year Master's student in Mathematics at Asian International University

Keywords:

Mittag-Leffler function, fractional analysis, asymptotic formula, Laplace transform, fractional differential equations, subdiffusion, complex plane.

Abstract

This scientific article analyzes the theoretical properties of the Mittag-Leffler function and its asymptotic expressions, which play an important role in fractional analysis and problems of mathematical physics. In particular, the definition of one- and two-parameter Mittag-Leffler functions, their relationship with Laplace transformations, and their role in the representation of solutions of fractional differential equations are highlighted. Also, the asymptotic behavior of this function in various domains of the complex plane is studied, and approximate estimates for large arguments are given. The obtained results serve for a deeper understanding of the mathematical foundations of subdiffusion processes, zero and nonlocal boundary value problems, as well as time-fraction models.

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References

Mittag, G., & Leffler, M. G. (1903). Sur la nouvelle fonction Eα(x). Comptes Rendus de l'Académie des Sciences de Paris, 137, 554–558.

Podlubny, I. (1999). Fractional Differential Equations. San Diego: Academic Press.

Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations. Elsevier.

Gorenflo, R., Kilbas, A. A., Mainardi, F., & Rogosin, S. V. (2014). Mittag–Leffler Functions, Related Topics and Applications. Springer.

Mainardi, F. (2010). Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. Imperial College Press.

Haubold, H. J., Mathai, A. M., & Saxena, R. K. (2011). Mittag-Leffler Functions and Their Applications. Journal of Applied Mathematics, 2011, Article ID 298628.

Diethelm, K. (2010). The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Springer.

Oldham, K. B., & Spanier, J. (1974). The Fractional Calculus. Academic Press.

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Published

2025-12-18

How to Cite

Sapayev Oybek Azadboy ugli. (2025). MITTAG-LEFLER FUNCTION AND ITS ASYMPTOTICS. Journal of Applied Science and Social Science, 15(12), 765–768. Retrieved from https://www.internationaljournal.co.in/index.php/jasass/article/view/2700

Issue

Vol. 15 No. 12 (2025): Volume 15 Issue 12

Section

Articles

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