Abstract
The space–time fractional diffusion equations on finite domain model anomalous diffusion behavior with large particle jumps combined with long waiting times. In this work we prove existence of strong solutions for such equations. Our proofs strongly depend on the fractional Sturm–Liouville theory, precisely on the problem of finding eigenvalues and corresponding eigenfunctions to the certain fractional differential equation. Using the method of separating variables and applying theorem ensuring existence of solutions to the fractional Sturm–Liouville problem we solve several types of fractional diffusion equations.
Please cite to this paper as published in: Fract. Calc. Appl. Anal., Vol. 19, No 2 (2016), pp. 516–550, DOI: 10.1515/fca-2016-0027
Acknowledgement
Research supported under Czestochowa University of Technology project BS/PB-1-105-3010/2011/S (M. Klimek), Bialystok University of Technology grant S/WI/1/16 (A.B. Malinowska) and by the Warsaw School of Economics grant KAE/S15/35/15 (T. Odzijewicz). The authors are grateful to Jacky Cresson for fruitful discussions during the Joint Meeting of the German Mathematical Society (DMV) and the Polish Mathematical Society (PTM), 17–20 September 2014, Pozna ǹ, Poland.
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© 2016 Diogenes Co., Sofia
Articles in the same Issue
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- Editorial
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- Survey Paper
- A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations
- Survey Paper
- A free fractional viscous oscillator as a forced standard damped vibration
- Research Paper
- On a Legendre Tau method for fractional boundary value problems with a Caputo derivative
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- Generalized fraction evolution equations with fractional Gross Laplacian
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- Nonlinear Riemann-Liouville fractional differential equations with nonlocal Erdelyi-Kober fractional integral conditions
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- Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity
- Research Paper
- Applications of the fractional Sturm-Liouville problem to the space-time fractional diffusion in a finite domain
- Short Paper
- Measurement of para-xylene diffusivity in zeolites and analyzing desorption curves using the Mittag-Leffler function
- Short Paper
- Monotonicity of functions and sign changes of their Caputo derivatives
- Short Note
- On the Volterra μ-functions and the M-Wright functions as kernels and eigenfunctions of Volterra type integral operators
Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA-Volume 19-2-2016)
- Survey Paper
- A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations
- Survey Paper
- A free fractional viscous oscillator as a forced standard damped vibration
- Research Paper
- On a Legendre Tau method for fractional boundary value problems with a Caputo derivative
- Research Paper
- Nonlinear Dirichlet problem with non local regional diffusion
- Research Paper
- Generalized fraction evolution equations with fractional Gross Laplacian
- Research Paper
- A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation
- Research Paper
- Convolutional approach to fractional calculus for distributions of several variables
- Research Paper
- Existence theorems for semi-linear Caputo fractional differential equations with nonlocal discrete and integral boundary conditions
- Research Paper
- Nonlinear Riemann-Liouville fractional differential equations with nonlocal Erdelyi-Kober fractional integral conditions
- Research Paper
- Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity
- Research Paper
- Applications of the fractional Sturm-Liouville problem to the space-time fractional diffusion in a finite domain
- Short Paper
- Measurement of para-xylene diffusivity in zeolites and analyzing desorption curves using the Mittag-Leffler function
- Short Paper
- Monotonicity of functions and sign changes of their Caputo derivatives
- Short Note
- On the Volterra μ-functions and the M-Wright functions as kernels and eigenfunctions of Volterra type integral operators