A Note On Fractional Integration
Branislav Martić (1973)
Publications de l'Institut Mathématique
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Displaying similar documents to “On fractional differentiation and integration on spaces of homogeneous type.”
A Note On Fractional Integration
On fractional derivatives
Helena Musielak (1973)
Colloquium Mathematicae
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On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)
Małgorzata Klimek (2011)
Banach Center Publications
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One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.
Vector-valued inequalities for the commutators of fractional integrals with rough kernels
Yanping Chen, Xinfeng Wu, Honghai Liu (2014)
Studia Mathematica
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Some conditions implying vector-valued inequalities for the commutator of a fractional integral and a fractional maximal operator are established. The results obtained are substantial improvements and extensions of some known results.
Some fractional integral formulas for the Mittag-Leffler type function with four parameters
Praveen Agarwal, Juan J. Nieto (2015)
Open Mathematics
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In this paper we present some results from the theory of fractional integration operators (of Marichev- Saigo-Maeda type) involving the Mittag-Leffler type function with four parameters ζ , γ, Eμ, ν[z] which has been recently introduced by Garg et al. Some interesting special cases are given to fractional integration operators involving some Special functions.
Large linear equation with left and right fractional derivatives in a finite interval
B. Stanković (2011)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Fractional Derivatives in Spaces of Generalized Functions
Stojanović, Mirjana (2011)
Fractional Calculus and Applied Analysis
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MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo We generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of...
Note on the fractional parts of λθⁿ
Masayoshi Hata (2005)
Acta Arithmetica
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On a sum of fractional parts
B. Martić (1964)
Matematički Vesnik
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On a Differential Equation with Left and Right Fractional Derivatives
Atanackovic, Teodor, Stankovic, Bogoljub (2007)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05 We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational principles with fractional derivatives. We reduce the problem to a Fredholm integral equation and construct a solution in the space of continuous functions. Two competing approaches in formulating differential equations...
Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
Choukri Derbazi, Hadda Hammouche (2021)
Mathematica Bohemica
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We study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to illustrate the main results.