The foam drainage equation with time and space-fractional derivatives solved by the adomian method.
Dahmani, Z., Mesmoudi, M.M., Bebbouchi, R. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Dahmani, Z., Mesmoudi, M.M., Bebbouchi, R. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Branislav Martić (1973)
Publications de l'Institut Mathématique
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Tadeusz Kaczorek, Kamil Borawski (2016)
International Journal of Applied Mathematics and Computer Science
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The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
B. Martić (1964)
Matematički Vesnik
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Helena Musielak (1973)
Colloquium Mathematicae
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Masayoshi Hata (2005)
Acta Arithmetica
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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.
Tadeusz Kaczorek (2016)
International Journal of Applied Mathematics and Computer Science
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Fractional descriptor reduced-order nonlinear observers for a class of fractional descriptor continuous-time nonlinear systems are proposed. Sufficient conditions for the existence of the observers are established. The design procedure for the observers is given and demonstrated on a numerical example.
Petráš, Ivo (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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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...
Amina Boucenna, Toufik Moussaoui (2014)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.
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.
Ayoub, N., Alzoubi, F., Khateeb, H., Al-Qadi, M., Hasan (Qaseer), M., Albiss, B., Rousan, A. (2006)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05 We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution...