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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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.
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...
Gülçin Bozkurt, Durmuş Albayrak, Neşe Dernek (2019)
Applications of Mathematics
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We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for...
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.
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.
Astha Chauhan, Rajan Arora (2019)
Communications in Mathematics
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In this work, the fractional Lie symmetry method is applied for symmetry analysis of time fractional Kupershmidt equation. Using the Lie symmetry method, the symmetry generators for time fractional Kupershmidt equation are obtained with Riemann-Liouville fractional derivative. With the help of symmetry generators, the fractional partial differential equation is reduced into the fractional ordinary differential equation using Erdélyi-Kober fractional differential operator. The conservation...