On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis
Copyright policy )On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis
We consider the time-fractional derivative in the Caputo sense of orderα∈(0, 1). Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function inR+, two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Moreover, the limit whenα↗1of the respective solutions is analyzed, recovering the solutions of the classical boundary-value problems whenα= 1, and the fractional diffusion equation becomes the heat equation.
- Austral University Argentina
- National Scientific and Technical Research Council Argentina
- National University of Rosario Argentina
FRACTIONAL DIFFUSION EQUATION, INITIAL BAUNDARY VALUE PROBLEM, Theory and Applications of Fractional Differential Equations, Caputo derivative, Numerical Methods for Singularly Perturbed Problems, QA1-939, FOS: Mathematics, https://purl.org/becyt/ford/1.1, Convection-Diffusion Problems, Reaction-Diffusion Equations, https://purl.org/becyt/ford/1, Anomalous Diffusion Modeling and Analysis, CAPUTO DERIVATIVE, Numerical Analysis, Time-Fractional Diffusion Equation, Applied Mathematics, Fractional partial differential equations, Algorithm, Fractional Derivatives, Boundary Value Problems, Modeling and Simulation, Physical Sciences, time-fractional diffusion equation, Mathematics, EXPLICIT SOLUTIONS
FRACTIONAL DIFFUSION EQUATION, INITIAL BAUNDARY VALUE PROBLEM, Theory and Applications of Fractional Differential Equations, Caputo derivative, Numerical Methods for Singularly Perturbed Problems, QA1-939, FOS: Mathematics, https://purl.org/becyt/ford/1.1, Convection-Diffusion Problems, Reaction-Diffusion Equations, https://purl.org/becyt/ford/1, Anomalous Diffusion Modeling and Analysis, CAPUTO DERIVATIVE, Numerical Analysis, Time-Fractional Diffusion Equation, Applied Mathematics, Fractional partial differential equations, Algorithm, Fractional Derivatives, Boundary Value Problems, Modeling and Simulation, Physical Sciences, time-fractional diffusion equation, Mathematics, EXPLICIT SOLUTIONS
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