Extended Mittag-Leffler Function and truncated $\nu$-fractional derivatives

arXiv1801.04995MaRDI QIDQ6296502

Gauhar Rahman, K. S. Nisar, Azeema, Abdul Ghaffar

Publication date: 3 January 2018

Abstract: The main objective of this article is to present $u$-fractional derivative $mu$-differentiable functions by considering 4-parameters extended Mittag-Leffler function (MLF). We investigate that the new $u$-fractional derivative satisfies various properties of order calculus such as chain rule, product rule, Rolle's and mean-value theorems for $mu$-differentiable function and its extension. Moreover, we define the generalized form of inverse property and the fundamental theorem of calculus and the mean-value theorem for integrals. Also, we establish a relationship with fractional integral through truncated $u$-fractional integral.

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Gamma, beta and polygamma functions (33B15) Generalized hypergeometric series, ({}_pF_q) (33C20) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Classical hypergeometric functions, ({}_2F_1) (33C05) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

This page was built for publication: Extended Mittag-Leffler Function and truncated $\nu$-fractional derivatives

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6296502)