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Integral equations involving generalized Mittag-Leffler function
Ukrains’kyi Matematychnyi Zhurnal, 2020 UDC 517.5 The paper deals with solving the integral equation with a generalized Mittag-Leffler function E α , β γ , q ( z ) that defines a kernel using a fractional integral operator. The existence of the solution is justified and necessary conditions on the integral equation admiting a solution are ...
Rachana Desai +2 more
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Generalization of Beta functions in terms of Mittag-Leffler function [PDF]
Frontiers in Scientific Research and Technology, 2020 In this paper, we give a new generalization of extended beta functions by using generalized Mittag Leffler functions. We investigate its properties and its integral representations. In addition, we establish the generalization of extended hypergeometric and Confluent hypergeometric functions by using the newly extended beta function. Some properties of
Karima Oraby +5 more
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Self-Similar Cauchy Problems and Generalized Mittag-Leffler Functions [PDF]
Fractional Calculus and Applied Analysis, 2021 By observing that the fractional Caputo derivative can be expressed in terms of a multiplicative convolution operator, we introduce and study a class of such operators which also have the same self-similarity property as the Caputo derivative. We proceed by identifying a subclass which is in bijection with the set of Bernstein functions and we provide ...
Patie, Pierre, Srapionyan, Anna
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INTEGRAL TRANSFORM WITH THE EXTENDED GENERALIZED MITTAG-LEFFLER FUNCTION
More Progresses in Analysis, 2006 he paper is devoted to the study of the integral transform containing the special function å((á, â) n ;z) generalizing the Mittag‐Leffler type function in the space £v,r (1 ≤ r ≤ 8, í ∈ R) of Lebesgue measurable functions on R+ = (0,+8) such that ‖ƒ‖ v,r < 8, where Mapping properties such as the boundedness, the range, the representation and the ...
Kilbas, A. A., Koroleva, A. A.
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Radii of starlikeness and convexity of generalized Mittag-Leffler functions [PDF]
, 2020 In this paper our aim is to find the radii of starlikeness and convexity of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic ...
Arpad Baricz +3 more
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Fractal and Fractional, 2022 In this paper, by adopting the classical method of proofs, we establish certain new Chebyshev and Grüss-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function. The main results are more general and
Wengui Yang
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Journal of Inequalities and Applications, 2019 The aim of this paper is to present the Hadamard and the Fejér–Hadamard integral inequalities for (h−m) $(h-m)$-convex functions due to an extended generalized Mittag-Leffler function.
Shin Min Kang +3 more
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Generalized Mittag-Leffler kernels and generalized scaling operators in Mittag-Leffler analysis
, 2021 Generalized scaling operators and generalized Gauss kernels are fundamental concepts in Gaussian analysis with application to path integrals and PDEs via the Feynman-Kac formula. In non-Gaussian analysis, particularly in Mittag-Leffler analysis, i.e., in
Ang Elyn Gumanoy +3 more
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Journal of Function Spaces, 2022 This paper is aimed at presenting the unified integral operator in its generalized form utilizing the unified Mittag-Leffler function in its kernel. We prove the boundedness of this newly defined operator.
Tingmei Gao +4 more
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A new generalization of Mittag-Leffler function via q-calculus [PDF]
Advances in Difference Equations, 2020 AbstractThe present paper deals with a new different generalization of the Mittag-Leffler function through q-calculus. We then investigate its remarkable properties like convergence, recurrence relation, integral representation, q-derivative formula, q-Laplace transformation, and image formula under q-derivative operator.
Raghib Nadeem +3 more
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