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General Fractional Integrals and Derivatives of Arbitrary Order [PDF]
Symmetry, 2021 In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented, and some important classes of the kernels that satisfy this condition are introduced.
Yuri Luchko
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Fuzzy Fractional Integral Equations Under Compactness Type Condition
Fractional Calculus and Applied Analysis, 2012 In this paper we study a fuzzy fractional integral equation. The fractional derivative is considered in the sense of Riemann-Liouville and we establish existence of the solutions of fuzzy fractional integral equations using the Hausdorff measure of ...
Sadia Arshad +2 more
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GENERALIZED HERMITE–HADAMARD INCLUSIONS FOR A GENERALIZED FRACTIONAL INTEGRAL
Rocky Mountain Journal of Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Budak, Hueseyin +2 more
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On generalization fractional integrals
Lobachevskii Journal of Mathematics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sarikaya, Mehmet Zeki +1 more
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A generalization of the concept of q-fractional integrals
Acta Mathematica Sinica, English Series, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rajković, Predrag M. +2 more
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A Theory of Fractional Integration for Generalized Functions
SIAM Journal on Mathematical Analysis, 1975In this paper, we develop a theory of fractional integration for certain classes of generalized functions and give one simple application.First, we introduce the appropriate spaces of testing-functions and generalized functions and state some of their basic properties.
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Hypergeometric Integral Equations of a General Kind and Fractional Integration
SIAM Journal on Mathematical Analysis, 1972Some integral equations with the kernels containing a confluent hypergeometric function in two variables are studied by the use of fractional integration. These equations include as special cases the hypergeometric integral equations as well as the confluent hypergeometric integral equations discussed by earlier authors.
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A class of fractional integral transforms: a generalization of the fractional Fourier transform
IEEE Transactions on Signal Processing, 2002The paper presents a systematic and unified approach to fractional integral transforms. We introduce a new class of fractional integral transforms that includes the fractional Fourier and Hankel transforms and the fractional integration and differentiation operators as special cases. These fractional transforms may also be viewed as angular transforms,
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Generalized fractional integrals on generalized Morrey spaces
Mathematische Nachrichten, 2013On generalized Morrey spaces with variable exponent and variable growth function the boundedness of generalized fractional integral operators is established, where . The result is a generalization of the theorems of Adams [1] (1975) and Gunawan [11] (2003). Moreover, we prove weak type boundedness.
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Generalized Fractional Integral Operator in a Complex Domain
Studia Universitatis Babes-Bolyai MatematicaA new fractional integral operator is used to present a generalized class of analytic functions in a complex domain. The method of definition is based on a Hadamard product of analytic function, which is called convolution product. Then we formulate a convolution integral operator acting on the sub-class of normalized analytic functions.
Dalia S. Ali +3 more
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