Related papers: Oscillatory integrals for Mittag-Leffler functions…
In this paper, we establish new an inequality of weighted Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.
The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler type functions. The justification of differentiation formulas is made by using the concept of the uniform…
We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired by the recent definition of spherical analyticity.
The problem of calculating the Mittag-Leffler function $E_{\rho,\mu} (z)$ is considered in the paper. To solve this problem integral representations for the function $E_{\rho,\mu}(z)$ are transformed in such a way that they could not…
In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the…
The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with…
The two-parameter Mittag-Leffler function $E_{\alpha, \beta}$ is of fundamental importance in fractional calculus. It appears frequently in the solutions of fractional differential and integral equations. Nonetheless, this vital function is…
Generalization of the integral representation of the gamma function has been obtained, which shows that the Hankel contour assumes rotation in the complex plane. The range of admissible values for the contour rotation angle is set. Using…
The study of the Mittag-Leffler function and its various generalizations has become a very popular topic in mathematics and its applications. In the present paper we prove the following estimate for the $q$-Mittag-Leffler function:…
This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…
We aim to introduce a new extension of Mittag-Leffler function via q-analogue and obtained their significant properties including integral representation, q-differentiation, q-Laplace transform, image formula under q-derivative operators.…
In this paper, we present an extension of Mittag-Leffler function by using the extension of beta functions (\"{O}zergin et al. in J. Comput. Appl. Math. 235 (2011), 4601-4610) and obtain some integral representation of this newly defined…
In this paper, a new estimate is obtained for the multinomial Mittag-Leffler function. This function was introduced by Yuri Luchko and Rudolfo Gorenflo as the fundamental solution of the ordinary differential equation of fractional discrete…
We prove a bilinear $L^2(\R^d) \times L^2(\R^d) \to L^2(\R^{d+1})$ estimate for a pair of oscillatory integral operators with different asymptotic parameters and phase functions satisfying a transversality condition. This is then used to…
Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about…
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…
We establish an $L^\infty\times L^2 \to L^2$ norm estimate for a bilinear oscillatory integral along parabolas incorporating oscillatory factors $e^{i|t|^{-\beta}}$.
In this paper, we establish some new Ostrowski's type inequalities for m- and (alpha,m)- logarithmically convex functions by using the Riemann-Liouville fractional integrals.
In recent years, the theory for Leibniz integral rule in the fractional sense has not been able to get substantial development. As an urgent problem to be solved, we study a Leibniz integral rule for Riemann-Liouville and Caputo type…
In this paper, we introduce the Levy density function as the limit of a generalized Mittag-Leffler density function. The fractional integral equation for the generalized Mittag-Leffler density function is also given. And the role of the…