On Euler methods for Caputo fractional differential equations

Petr Tomášek

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Displaying similar documents to “On Euler methods for Caputo fractional differential equations”

On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method

Haci Mehmet Baskonus, Hasan Bulut (2015)

Open Mathematics

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In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate...

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term.

Yang, Qianqian, Liu, Fawang, Turner, Ian (2010)

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An effective numerical method and its utilization to solution of fractional models used in bioengineering applications.

Petráš, Ivo (2011)

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The foam drainage equation with time and space-fractional derivatives solved by the adomian method.

Dahmani, Z., Mesmoudi, M.M., Bebbouchi, R. (2008)

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Fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative

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.

Weak solvability and numerical analysis of a class of time-fractional hemivariational inequalities with application to frictional contact problems

Mustapha Bouallala (2024)

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We investigate a generalized class of fractional hemivariational inequalities involving the time-fractional aspect. The existence result is established by employing the Rothe method in conjunction with the surjectivity of multivalued pseudomonotone operators and the properties of the Clarke generalized gradient. We are also exploring a numerical approach to address the problem, utilizing both spatially semi-discrete and fully discrete finite elements, along with a discrete approximation...

Numerical simulation of a point-source initiated flame ball with heat losses

Jacques Audounet, Jean-Michel Roquejoffre, Hélène Rouzaud (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.

A Note On Fractional Integration

Branislav Martić (1973)

Publications de l'Institut Mathématique

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Numerical solutions to integral equations equivalent to differential equations with fractional time

Bartosz Bandrowski, Anna Karczewska, Piotr Rozmej (2010)

International Journal of Applied Mathematics and Computer Science

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This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.

A constructive approach for solving system of fractional differential equations

H.R. Marasi, Vishnu Narayan Mishra, M. Daneshbastam (2017)

Waves, Wavelets and Fractals

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In this paper to solve a set of linear and nonlinear fractional differential equations, we modified the differential transform method. Adomian polynomials helped taking care of the non-linear terms. The main advantage of our algorithm over the numerical methods is being able to solve nonlinear systems without any discretization or restrictive assumption. We considered Caputo definition for fractional derivatives.

Duplication in a model of rock fracture with fractional derivative without singular kernel

Emile F. Doungmo Goufo, Morgan Kamga Pene, Jeanine N. Mwambakana (2015)

Open Mathematics

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We provide a mathematical analysis of a break-up model with the newly developed Caputo-Fabrizio fractional order derivative with no singular kernel, modeling rock fracture in the ecosystem. Recall that rock fractures play an important role in ecological and geological events, such as groundwater contamination, earthquakes and volcanic eruptions. Hence, in the theory of rock division, especially in eco-geology, open problems like phenomenon of shattering, which remains partially unexplained...