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Fractional calculus and application of generalized Struve function.

Kottakkaran Sooppy Nisar1, Dumitru Baleanu2, Maysaa' Mohamed Al Qurashi3

  • 1Department of Mathematics, College of Arts and Science, Prince Sattam Bin Abdulaziz University, 11991 Wadi Aldawser, Saudi Arabia.

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|July 8, 2016
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Summary

A novel generalized Galué type Struve function (GTSF) was introduced. This new function aids in solving fractional kinetic equations, offering broader applications in mathematical sciences.

Keywords:
Fractional calculusFractional kinetic equationsGeneralized Struve functionIntegral transformsLaplace transforms

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Area of Science:

  • Mathematical Analysis
  • Fractional Calculus
  • Special Functions

Background:

  • Struve functions are essential in various mathematical and physical applications.
  • Generalizations of special functions are crucial for expanding their applicability.
  • Fractional kinetic equations model complex phenomena in diverse scientific fields.

Purpose of the Study:

  • To define and investigate a new generalization of Struve functions, termed the generalized Galué type Struve function (GTSF).
  • To apply integral operators with Appell's or Horn's functions to the GTSF.
  • To present solutions for fractional kinetic equations using the newly defined GTSF.

Main Methods:

  • Definition of the generalized Galué type Struve function (GTSF).
  • Application of integral operators involving Appell's functions and Horn's function.
  • Expressing results in terms of the Fox-Wright function.
  • Deriving solutions for fractional kinetic equations.

Main Results:

  • The integral operators applied to the GTSF yield results expressible via the Fox-Wright function.
  • The generalized GTSF provides a unified framework for solving various fractional kinetic equations.
  • New and familiar fractional kinetic equations can be investigated using this generalized function.

Conclusions:

  • The generalized Galué type Struve function (GTSF) is a powerful tool for extending the study of special functions.
  • The GTSF facilitates the analysis and solution of a wide range of fractional kinetic equations.
  • This generalization has significant implications for applied mathematical sciences and problem-solving.