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General fractional integral inequalities for convex and m-convex functions via an extended generalized Mittag-Leffler function [PDF]
Journal of Inequalities and Applications, 2018 In this paper some new general fractional integral inequalities for convex and m-convex functions by involving an extended Mittag-Leffler function are presented. These results produce inequalities for several kinds of fractional integral operators.
G. Farid +4 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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The Study of Fractional Quadratic Integral Equations Involves General Fractional Integrals
Fractal and FractionalThis paper investigates the well-posedness of analytical solutions to fractional quadratic differential equations, which involve generalized fractional integrals with respect to other functions.
Mi Zhou +3 more
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Generalized proportional fractional integral Hermite–Hadamard’s inequalities [PDF]
Advances in Difference Equations, 2021 AbstractThe theory of fractional integral inequalities plays an intrinsic role in approximation theory also it has been a key in establishing the uniqueness of solutions for some fractional differential equations. Fractional calculus has been found to be the best for modeling physical and engineering processes.
Tariq A. Aljaaidi +5 more
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General Fractional Vector Calculus
Mathematics, 2021 A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators.
Vasily E. Tarasov
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Fractional Minkowski-Type Integral Inequalities via the Unified Generalized Fractional Integral Operator [PDF]
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. A fractional integral operator comprising a unified Mittag-Leffler function is used to establish further Minkowski-type integral inequalities ...
Tingmei Gao +4 more
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General Fractional Integrals and Derivatives with the Sonine Kernels
Mathematics, 2021 In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero.
Yuri Luchko
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Fractional generalization of Kac integral [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2008 Generalization of the Kac integral and Kac method for paths measure based on the Levy distribution has been used to derive fractional diffusion equation. Application to nonlinear fractional Ginzburg-Landau equation is discussed.
Tarasov, Vasily E., Zaslavsky, George M.
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Generalized Fractional-Order Discrete-Time Integrator [PDF]
Complexity, 2017 We investigate a generalization of discrete-time integrator. Proposed linear discrete-time integrator is characterised by the variable, fractional order of integration/summation. Graphical illustrations of an analysis of particular vector matrices are presented. In numerical examples, we show relations between the order functions and element responses.
Dorota Mozyrska, Piotr Ostalczyk
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E. R. LOVE TYPE LEFT FRACTIONAL INTEGRAL INEQUALITIES
Проблемы анализа, 2020 Here first we derive a general reverse Minkowski integral inequality. Then motivated by the work of E. R. Love [4] on integral inequalities we produce general reverse and direct integral inequalities.
G. A. Anastassiou
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