Results 31 to 40 of about 13,688 (264)
Generalizations of some fractional integral inequalities via generalized Mittag-Leffler function
Journal of Inequalities and Applications, 2017 Fractional inequalities are useful in establishing the uniqueness of solution for partial differential equations of fractional order. Also they provide upper and lower bounds for solutions of fractional boundary value problems.
Ghulam Abbas +3 more
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Fractional integrals of generalized functions [PDF]
Journal of the Australian Mathematical Society, 1972 The concept of integrals of fractional order of a function f, defined by if Reα > 0, can be extended to generalised functions in the framework of the theory of convolution of distributions. The resulting theory [2, Chap. I §5.5] is very satisfactory for many purposes but there are circumstances in which it is not suitable.
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New applications of the new general integral transform method with different fractional derivatives
Alexandria Engineering Journal, 2023 Integral transforms are a versatile mathematical technique that can be applied in a wide range of science and engineering fields. We consider the general integral transform with the Caputo derivative and Constant Proportional Caputo derivative in this ...
Ali Akgül +4 more
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ON GENERALIZED FRACTIONAL INTEGRALS
Taiwanese Journal of Mathematics, 2001 The author introduces generalized fractional integrals and extends the Hardy-Littlewood-Sobolev theorem to Orlicz spaces. He also investigates the boundedness of generalized fractional integrals from Orlicz spaces to \(\text{BMO}_\varphi(\mathbb{R}^n)\) and from \(\text{BMO}_\varphi(\mathbb{R}^n)\) to \(\text{BMO}_\psi(\mathbb{R}^n)\), where \(\text ...
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Journal of Inequalities and Applications, 2019 In the article, we establish some new general fractional integral inequalities for exponentially m-convex functions involving an extended Mittag-Leffler function, provide several kinds of fractional integral operator inequalities and give certain special
Saima Rashid +4 more
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Analysis of the family of integral equation involving incomplete types of I and Ī-functions
Applied Mathematics in Science and Engineering, 2023 The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete $ \bar {I} $ -function (I $ \bar {I} $ F) in its kernel.
Sanjay Bhatter +5 more
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More General Weighted-Type Fractional Integral Inequalities via Chebyshev Functionals
Fractal and Fractional, 2021 The purpose of this research paper is first to propose the generalized weighted-type fractional integrals. Then, we investigate some novel inequalities for a class of differentiable functions related to Chebyshev’s functionals by utilizing the proposed ...
Gauhar Rahman +4 more
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A new Generalized fractional derivative and integral
, 2017 In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional derivative such as Product Rule, Quotient Rule, Chain Rule, Roll's Theorem and Mean Value Theorem.
AKKURT, Abdullah +2 more
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On generalized some integral inequalities for local fractional integrals
Applied Mathematics and Computation, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mehmet Zeki Sarikaya +2 more
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General Fractional Calculus: Multi-Kernel Approach
Mathematics, 2021 For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
Vasily E. Tarasov
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