Results 21 to 30 of about 6,121,976 (240)
Mathematics, 2022 In this article, we investigate the existence and uniqueness of solutions for a nonlinear coupled system of Liouville–Caputo type fractional integro-differential equations supplemented with non-local discrete and integral boundary conditions.
Muthaiah Subramanian +4 more
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Elements of fractional calculus. Fractional integrals [PDF]
, 2022 The paper is devoted to the basic properties of fractional integrals. It is a survey of the well-known properties of fractional integrals, however, the authors tried to present the known information about fractional integrals as short and transparently ...
Мішура, Юлія С. +5 more
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Generalized Fractional Integral Operators on Generalized Local Morrey Spaces [PDF]
Journal of Function Spaces, 2015 We study the continuity properties of the generalized fractional integral operatorIρon the generalized local Morrey spacesLMp,φ{x0}and generalized Morrey spacesMp,φ. We find conditions on the triple(φ1,φ2,ρ)which ensure the Spanne-type boundedness ofIρfrom one generalized local Morrey spaceLMp,φ1{x0}to anotherLMq,φ2{x0},1<p<q<∞, and fromLM1,φ1{
Guliyev, V. S. +3 more
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General Fractional Noether Theorem and Non-Holonomic Action Principle
Mathematics, 2023 Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non ...
Vasily E. Tarasov
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Zhejiang Daxue xuebao. Lixue ban, 2018 Based on the theory of local fractional calculus on fractal sets,the author established an identity involving local fractional integrals. Using the identity, some generalized Ostrowski type inequalities for generalized harmonically s-convex functions ...
SUNWenbing(孙文兵)
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Singular and Fractional Integral Operators on Weighted Local Morrey Spaces
Journal of Fourier Analysis and Applications, 2022 We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calderón-Zygmund operators suitably defined on the functions of the space.
Javier Duoandikoetxea, Marcel Rosenthal
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Fractal and Fractional, 2022 The present paper provides several corrected dual-Simpson-type inequalities for functions whose local fractional derivatives are generalized convex. To that end, we derive a new local fractional integral identity as an auxiliary result.
Abdelghani Lakhdari +3 more
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Two-weight Norm Inequalities for Local Fractional Integrals on Gaussian Measure Spaces [PDF]
, 2021 In this paper, the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights. More precisely, the authors first obtain the two-weight
Di, Boning, Yan, Dunyan, He, Qianjun
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About fractional integrals in the space of locally integrable functions
Journal of Mathematical Analysis and Applications, 1992 The authors show that the largest ``natural'' function space, where the Riemann-Liouville fractional integral operator \[ J^ \alpha f(x)={1\over{\Gamma(\alpha)}} \int_ 0^ x (x-t)^{\alpha-1} f(t)dt \] and differential operator \[ D^ \alpha f(x)={1 \over{\Gamma(1-\alpha)}} {d \over dx} \int_ 0^ x (x-t)^{-\alpha} f(t)dt ...
Martinez, Celso +2 more
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Nonlocal Probability Theory: General Fractional Calculus Approach
Mathematics, 2022 Nonlocal generalization of the standard (classical) probability theory of a continuous distribution on a positive semi-axis is proposed. An approach to the formulation of a nonlocal generalization of the standard probability theory based on the use of ...
Vasily E. Tarasov
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