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Note on generalized Mittag-Leffler function.

Rachana Desai1, I A Salehbhai2, A K Shukla3

  • 1Department of Mathematics, K. J. Somaiya College of Engineering, Vidyavihar, Mumbai, 400077 India.

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Summary
This summary is machine-generated.

This study explores a generalized Mittag-Leffler function and its associated fractional operator within Lebesgue measurable functions. The research details the composition of this operator with the Riemann-Liouville fractional integration operator.

Keywords:
Fractional CalculusGeneralized Mittag-Leffler function

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Area of Science:

  • Fractional Calculus
  • Analysis

Background:

  • Mittag-Leffler functions are crucial in fractional calculus.
  • Fractional operators are essential tools for modeling complex systems.

Purpose of the Study:

  • To investigate a generalized Mittag-Leffler function.
  • To analyze an associated fractional operator in Lebesgue spaces.
  • To determine the composition of this operator with the Riemann-Liouville fractional integration operator.

Main Methods:

  • The study utilizes concepts from real analysis and fractional calculus.
  • The fractional operator is defined and discussed within the space of Lebesgue measurable functions.
  • Composition properties are derived using established fractional calculus techniques.

Main Results:

  • A generalized Mittag-Leffler function is studied.
  • Properties of a novel fractional operator are established.
  • The composition of the generalized fractional operator with the Riemann-Liouville fractional integration operator is successfully obtained.

Conclusions:

  • The research contributes to the understanding of generalized Mittag-Leffler functions and their associated operators.
  • The findings provide a foundation for further applications in fractional differential equations and modeling.
  • The composition results offer new insights into the behavior of fractional integration.