Results 251 to 260 of about 5,959,720 (288)

On Properties of an Entire Function That is a Generalization of the Wright Function

Journal of Mathematical Sciences, 2020
The author considers the function \[\Theta_{n,\alpha}(z;\mu)=\sum_{k=0}^\infty \frac{\sin n\omega_k}{\sin \omega_k}\, \frac{z^k}{k! \Gamma(\mu-\frac{\alpha k}{2n})}, \qquad \omega_k:=(k+1)\pi/(2n)\] for positive integer \(n\). This is a fundamental solution of the fractional differential equation \[\frac{\partial^\alpha u}{\partial t^\alpha}+(-1)^n ...
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The Classical Wright Function

2020
This chapter deals with the classical Wright function. Like the functions of Mittag-Leffler type, the functions of Wright type are known to play fundamental roles in various applications of the fractional calculus. This is mainly due to the fact that they are interrelated with the Mittag-Leffler functions through Laplace and Fourier transformations.
Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei Rogosin   +3 more
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Functional inequalities for the Wright functions

Integral Transforms and Special Functions, 2016
ABSTRACTIn this paper, our aim is to show some mean value inequalities for the Wright function, such as Turan-type inequalities, Lazarevic-type inequalities, Wilker-type inequalities and Redheffer-type inequalities. Moreover, we prove monotonicity of ratios for sections of series of Wright functions, the result is also closely connected with Turan-type
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Contiguous relations for the Fox–Wright function

Journal of Mathematical Analysis and Applications, 2019
The writing is very clear and generally easy to follow. The goal of the paper is to introduce the concept that contiguous relations are an effective tool for handling hypergeometric functions. Four different kinds of contiguous relations for the Fox-Wright function are provided in this paper.
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Mittag-Leffler and Wright Functions

2021
The exponential function \(e^z\) plays an extremely important role in the theory of integer-order differential equations. For fdes, its role is subsumed by the Mittag-Leffler and Wright functions. In this chapter, we discuss their basic analytic properties and numerical computation.
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On the distribution of zeros of the wright function

Integral Transforms and Special Functions, 2001
The paper deals with the distribution of zeros of the Wright function in the case ρ > −1and the parameter β is a real number. The exact formulae for the order, the type and the indicator function of the entire function φ (ρ, β; z ) are given. On the basis of these results this function is shown to be a function of completely regular growth.
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On the stability of Wright-convex functions

aequationes mathematicae, 2003
Let \(D\) be a convex subset of a linear space. A function \(f:D\to{\mathbb R}\) is called Wright-convex if \[ f\bigl(tx+(1-t)y\bigr)+f\bigl(ty+(1-t)x\bigr)\leq f(x)+f(y) \] for all \(x,y\in D\), \(t\in[0,1]\). The main result of the paper is the following Theorem: Let \(D\subset{\mathbb R}^N\) be a nonempty open and convex set and let \(\delta\geq 0\).
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Certain properties of the Wright function

Journal of Interdisciplinary Mathematics
In this paper, we have demonstrated several results for the Wright functions. We studied some basic properties, successive differentiation recurrence relations, various types of integral representations, integral duplication formulae, multiplication theorem, etc.
Bhaven V. Zala, Jyotindra C. Prajapati
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The function of the Wright type in fractional calculus

2010
We provide a survey of the high transcendental functions known in the literature as Wright functions. We devote particular attention for two functions of the Wright type, which, in virtue of their role in applications of fractional calculus, we have called auxiliary functions.
MAINARDI, FRANCESCO, A. Mura, G. Pagnini
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A continuity result on $t$-Wright-convex functions

Publicationes Mathematicae Debrecen, 2003
Let \(I\subset\mathbb{R}\) be a non-void open interval and \(t \in I\) be fixed. A function \(f:I \to \mathbb{R}\) is called \(t\)-Wright-convex if \[ f(tx+(1-t)y)+f((1-t)x+ty)\leq f(x)+f(y) \] holds for all \(x,y\in I.\) It is known that there exist discontinuous \(t\)-Wright-convex functions defined on the whole \(\mathbb{R}\) that are bounded above.
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