Extended Mittag-Leffler Function and truncated ν-fractional derivatives

2018/01/03 by Abdul Ghaffar, Gauhar Rahman, Ghaffar, A. +5
Mathematics · #Fractional Differential Equations Solutions #Mathematical Inequalities and Applications #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1801.04995

Abstract

The main objective of this article is to present ν-fractional derivative μ-differentiable functions by considering 4-parameters extended Mittag-Leffler function (MLF). We investigate that the new ν-fractional derivative satisfies various properties of order calculus such as chain rule, product rule, Rolle's and mean-value theorems for μ-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 ν-fractional integral.

Related

• Mittag-Leffler functions and the truncated V-fractional derivative
• On the local M-derivative
• A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties
• A truncated V-fractional derivative in ℝⁿ
• Fractional calculus and generalized Mittag-Leffler type functions