Geometric Properties of a Certain Class of Mittag–Leffler-Type Functions
Reads0
Chats0
TLDR
In this paper , sufficient conditions were established for a class of normalized Mittag-Leffler-type functions to satisfy several geometric properties such as star-likeness, convexity, close-to-convexity and uniform convexness inside the unit disk.Abstract:
The main objective of this paper is to establish some sufficient conditions so that a class of normalized Mittag–Leffler-type functions satisfies several geometric properties such as starlikeness, convexity, close-to-convexity, and uniform convexity inside the unit disk. Moreover, pre-starlikeness and k-uniform convexity are discussed for these functions. Some sufficient conditions are also derived so that these functions belong to the Hardy spaces Hp and H∞. Furthermore, the inclusion properties of some modified Mittag–Leffler-type functions are discussed. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section.read more
Citations
More filters
Journal ArticleDOI
A comparative study of the stability of some fractional-order cobweb economic models
Journal ArticleDOI
The Mittag-Leffler Function for Re-Evaluating the Chlorine Transport Model: Comparative Analysis
TL;DR: In this paper , a variable order partial derivative is incorporated for describing the chlorine transport system, and an analytical solution via Mittag-Leffler functions is introduced to solve the transport model with non-integer order derivative.
Journal ArticleDOI
Generalization of Some Fractional Integral Operator Inequalities for Convex Functions via Unified Mittag-Leffler Function
TL;DR: In this article , the Hermite-Hadamard inequality for integral operators with Mittag-Leffler functions is established using the closely symmetric property for (α,m)-convex functions.
Journal ArticleDOI
Some Properties of Bazilevič Functions Involving Srivastava-Tomovski Operator
TL;DR: In this article , a new class of Bazilevič functions involving the Srivastava-Tomovski generalization of the Mittag-Leffler function is introduced.
Journal ArticleDOI
More on the Unified Mittag-Leffler Function
TL;DR: In this article, the authors investigated the relationship of unified Mittag-Leffler function with some known special functions and obtained some integral transforms in terms of Wright generalized function and established a recurrence relation along with another important result.
References
More filters
Journal ArticleDOI
Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena
TL;DR: In this article, the authors introduced fractional derivatives of order α in time, with 0 for relaxation, diffusion, oscillations, and wave propagation, and showed that they are governed by simple differential equations of order 1 and 2 in time.
A singular integral equation with a generalized mittag leffler function in the kernel
TL;DR: In this article, a linear operator of order functions of order (1.2) is defined and an operator of fractional integration is employed to prove results on the solutions of the integral equation.
Journal ArticleDOI
On uniformly convex functions
TL;DR: In this article, a new class of normalized functions regular and univalent in the unit disk are introduced, called uniformly convex functions, which are dened by a purely geometric property and obtained a few theorems about this new class and point out a number of open problems.