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.
Sandeep P. Bhairat, Dnyanoba-Bhaurao Dhaigude (2019)
Mathematica Bohemica
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This paper is devoted to studying the existence of solutions of a nonlocal initial value problem involving generalized Katugampola fractional derivative. By using fixed point theorems, the results are obtained in weighted space of continuous functions. Illustrative examples are also given.
B. Martić (1964)
Matematički Vesnik
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Masayoshi Hata (2005)
Acta Arithmetica
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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.
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.
Helena Musielak (1973)
Colloquium Mathematicae
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Aurelian Cernea (2016)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.
Branislav Martić (1973)
Publications de l'Institut Mathématique
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Marko Kostić (2018)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, we investigate a class of abstract degenerate fractional differential equations with Caputo derivatives. We consider subordinated fractional resolvent families generated by multivalued linear operators, which do have removable singularities at the origin. Semi-linear degenerate fractional Cauchy problems are also considered in this context.
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.
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...
Benchohra, Mouffak, Hamani, Samira, Ntouyas, Sotiris K. (2008)
Surveys in Mathematics and its Applications
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Mouffak Benchohra, Samira Hamani (2008)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.