Discrete fractional calculus with the nabla operator.
Atici, F.M., Eloe, P. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Atici, F.M., Eloe, P. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Lv Zhanmei, Gong Yanping, Chen Yi (2014)
Applications of Mathematics
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The paper deals with a class of discrete fractional boundary value problems. We construct the corresponding Green's function, analyse it in detail and establish several of its key properties. Then, by using the fixed point index theory, the existence of multiple positive solutions is obtained, and the uniqueness of the solution is proved by a new theorem on an ordered metric space established by M. Jleli, et al. (2012).
Ferreira, Rui A.C. (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Li, Changpin, Qian, Deliang, Chen, Yangquan (2011)
Discrete Dynamics in Nature and Society
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Yakar, Coşkun (2010)
Abstract and Applied Analysis
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Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
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Benchohra, Mouffak, Hamani, Samira, Ntouyas, Sotiris K. (2008)
Surveys in Mathematics and its Applications
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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.
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...
Herzallah, Mohamed A.E., Baleanu, Dumitru (2011)
Advances in Difference Equations [electronic only]
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Natthaphong Thongsalee, Sorasak Laoprasittichok, Sotiris K. Ntouyas, Jessada Tariboon (2015)
Open Mathematics
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In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.
Babakhani, Azizollah, Baleanu, Dumitru (2011)
Advances in Difference Equations [electronic only]
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