Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case 1 ... s ... n/p.
Winfried Sickel (1997)
Forum mathematicum
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Displaying similar documents to “Fractional Hajłasz-Morrey-Sobolev spaces on quasi-metric measure spaces”
Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case 1 ... s ... n/p.
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.
A Note On Fractional Integration
Branislav Martić (1973)
Publications de l'Institut Mathématique
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On a sum of fractional parts
B. Martić (1964)
Matematički Vesnik
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Note on the fractional parts of λθⁿ
Masayoshi Hata (2005)
Acta Arithmetica
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Generalized Fractional Calculus With Application in Mechanics
Ljubica Oparnica (2002)
Matematički Vesnik
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IVPs for singular multi-term fractional differential equations with multiple base points and applications
Yuji Liu, Pinghua Yang (2014)
Applicationes Mathematicae
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The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term...
Mild solution of fractional order differential equations with not instantaneous impulses
Pei-Luan Li, Chang-Jin Xu (2015)
Open Mathematics
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In this paper, we investigate the boundary value problems of fractional order differential equations with not instantaneous impulse. By some fixed-point theorems, the existence results of mild solution are established. At last, one example is also given to illustrate the results.
A Poster about the Recent History of Fractional Calculus
Machado, Tenreiro, Kiryakova, Virginia, Mainardi, Francesco (2010)
Fractional Calculus and Applied Analysis
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MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22 In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major contributions during the period 1966-2010.
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.
Weighted norm inequalities for multilinear fractional operators on Morrey spaces
Takeshi Iida, Enji Sato, Yoshihiro Sawano, Hitoshi Tanaka (2011)
Studia Mathematica
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A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered.
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...