Fractional Differential Operator of Generalized Mittag-Leffler Function Using Jacobi Polynomial


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Authors

  • Aakansha Vyas Department of Mathematics, Mewar University, Chittorgarh, Rajasthan, India
  • P. K. Mishra Department of Mathematics, Jodhpur Institute of Engineering & Technology, Jodhpur, Rajasthan, India

Keywords:

Generalized Mittag-Leffler function, Generalized Fractional Calculus, Generalized Wright function, Jacoby Polynomial

Abstract

The paper is devoted to the study of generalized fractional calculus of the generalized Mittag-Leffler function $E^{\delta } _{\upsilon ,\rho } \left(z\right)$ which is an entire function of the form \[E^{\delta } _{\upsilon ,\rho } \left(z\right)=\sum\limits_{s=0}^{\infty } \frac{\left(\delta \right)_{s} z^{s} }{{\rm \Gamma }\left(\upsilon s+\rho \right)\; s!} \] Where $\upsilon >0$ and $\rho >0$. For $\delta =1$, it is reduces to Mittag-Leffler function $E_{\upsilon ,\rho } \left(z\right)$. We have shown that the generalized fractional calculus operators transform such function with power multipliers in to generalized Wright function. Some elegant results obtained by Kilbas and Saigo [11], Saxena and Saigo [24] are the special cases of the result derived in this paper.

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Published

15-03-2019

How to Cite

Aakansha Vyas, & P. K. Mishra. (2019). Fractional Differential Operator of Generalized Mittag-Leffler Function Using Jacobi Polynomial. International Journal of Mathematics And Its Applications, 7(1), 15–22. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/264

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Section

Research Article