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@article{IJAMCS_2023_33_3_a0,
author = {Malinowska, Agnieszka B. and Odzijewicz, Tatiana and Poskrobko, Anna},
title = {Applications of the fractional {Sturm-Liouville} difference problem to the fractional diffusion difference equation},
journal = {International Journal of Applied Mathematics and Computer Science},
pages = {349--359},
publisher = {mathdoc},
volume = {33},
number = {3},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_3_a0/}
}
TY - JOUR AU - Malinowska, Agnieszka B. AU - Odzijewicz, Tatiana AU - Poskrobko, Anna TI - Applications of the fractional Sturm-Liouville difference problem to the fractional diffusion difference equation JO - International Journal of Applied Mathematics and Computer Science PY - 2023 SP - 349 EP - 359 VL - 33 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_3_a0/ LA - en ID - IJAMCS_2023_33_3_a0 ER -
%0 Journal Article %A Malinowska, Agnieszka B. %A Odzijewicz, Tatiana %A Poskrobko, Anna %T Applications of the fractional Sturm-Liouville difference problem to the fractional diffusion difference equation %J International Journal of Applied Mathematics and Computer Science %D 2023 %P 349-359 %V 33 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_3_a0/ %G en %F IJAMCS_2023_33_3_a0
Malinowska, Agnieszka B.; Odzijewicz, Tatiana; Poskrobko, Anna. Applications of the fractional Sturm-Liouville difference problem to the fractional diffusion difference equation. International Journal of Applied Mathematics and Computer Science, Tome 33 (2023) no. 3, pp. 349-359. http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_3_a0/
[1] [1] Abdeljawad, T. (2011). On Riemann and Caputo fractional differences, Computers and Mathematics with Applications 62(3): 1602-1611.
[2] [2] Almeida, R., Malinowska, A.B., Morgado, M.L. and Odzijewicz, T. (2017). Variational methods for the solutions of fractional discrete/continuous Sturm-Liouville problems, Journal of Mechanics of Materials and Structures 12(1): 3-21.
[3] [3] Atici, F. and Eloe, P.W. (2009). Initial value problems in discrete fractional calculus, Proceedings of the American Mathematical Society 137(3): 981-989.
[4] [4] Bayrak, M.A., Demir, A. and Ozbilge, E. (2020). Numerical solution of fractional diffusion equation by Chebyshev collocation method and residual power series method, Alexandria Engineering Journal 59(6): 4709-4717.
[5] [5] Ciesielski, M., Klimek, M. and Blaszczyk, T. (2017). The fractional Sturm-Liouville problem-numerical approximation and application in fractional diffusion, Journal of Computational and Applied Mathematics 317(6): 573-588.
[6] [6] Cresson, J., Jiménez, F. and Ober-Blobaum, S. (2021). Modelling of the convection-diffusion equation through fractional restricted calculus of variations, IFAC Papers Online 54(9): 482-487.
[7] [7] D’Ovidio, M. (2012). From Sturm-Liouville problems to fractional anomalous diffusion, Stochastic Processes and Their Applications 122(10): 3513-3544.
[8] [8] Goodrich, C. and Peterson, A.C. (2015). Discrete Fractional Calculus, Springer, Cham.
[9] [9] Hanert, E. and Piret, C. (2012). Numerical solution of the space-time fractional diffusion equation: Alternatives to finite differences, Proceedings of the 5th Symposium on Fractional Differentiation and Its Applications, Hohai, China.
[10] [10] Kaczorek, T. (2011). Selected Problems of Fractional Systems Theory, Lecture Notes in Control and Information Sciences, Vol. 411, Springer, Berlin/Heidelberg.
[11] [11] Kaczorek, T. (2018). Stability of interval positive fractional discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 28(3): 451-456, DOI: 10.2478/amcs-2018-0034.
[12] [12] Kaczorek, T. (2019). Positivity of fractional descriptor linear discrete-time systems, International Journal of Applied Mathematics and Computer Science 29(2): 305-310, DOI: 10.2478/amcs-2019-0022.
[13] [13] Klimek, M., Malinowska, A. B. and Odzijewicz, T. (2016). Applications of the Sturm-Liouville problem to the space-time fractional diffusion in a finite domain, Fractional Calculus and Applied Analysis 19(2): 516-550.
[14] [14] Lin, Y. and Xu, C. (2007). Finite difference/spectral approximations for the time-fractional diffusion equation, Journal of Computational Physics 225(2): 1533-1552.
[15] [15] Meerschaert, M.M. (2011). Fractional calculus, anomalous diffusion, and probability, in J. Klafter et al. (Eds), Fractional Dynamics: Recent Advances, World Scientific Publishing, Hackensack, pp. 265-284.
[16] [16] Meerschaert, M.M. and Tadjeran, C. (2004). Finite difference approximations for fractional advection-diffusion flow equations, Journal of Computational and Applied Mathematics 172(1): 65-77.
[17] [17] Metzler, R. and Klafter, J. (2000). The random walk’s guide to anomalous diffusion: A fractional dynamics approach, Physics Reports 339(1): 1-77.
[18] [18] Miller, K.S. and Ross, B. (1989). Fractional difference calculus, in H.M Srivastava and S. Owa (Eds), Univalent Functions, Fractional Calculus, and Their Application, Ellis Horwood, Chichester, pp. 139-152.
[19] [19] Mozyrska, D. and Girejko, E. (2013). Overview of fractional h-difference operators, in A. Almeida et al. (Eds), Operator Theory: Advances and Applications, Springer, Basel, pp. 253-268.
[20] [20] Mozyrska, D., Girejko, E. and Wyrwas, M. (2013). Comparison of h-difference fractional operators, in W. Mitkowski et al. (Eds), Advances in the Theory of Non-integer Order Systems, Lecture Notes in Electrical Engineering, Vol. 257, Springer, Heidelberg, pp. 192-198.
[21] [21] Mozyrska, D. and Wyrwas, M. (2015). The Z-transform method and Delta type fractional difference operators, Discrete Dynamics in Nature and Society 2015, Article ID: 852734, DOI: 10.1155/2015/852734.
[22] [22] Ostalczyk, P. (2008). Outline of Fractional-Order Differential-Integral Calculus: Theory and Applications in Automatic Control, Łódź University of Technology Press, Łódź, (in Polish).
[23] [23] Ostalczyk, P. (2012). Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains, International Journal of Applied Mathematics and Computer Science 22(3): 533-538, DOI: 10.2478/v10006-012-0040-7.
[24] [24] Ostalczyk, P. (2015). Discrete Fractional Calculus: Applications in Control and Image Processing, World Scientific Publishing, Singapore.
[25] [25] Płociniczak, L. (2019). Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting, Communications in Nonlinear Science and Numerical Simulation 76(9): 66-70.
[26] [26] Płociniczak, L. and Świtała (2022). Numerical scheme for Erdélyi-Kober fractional diffusion equation using Galerkin-Hermite method, Fractional Calculus and Applied Analysis 25(4): 1651-1687.
[27] [27] Płociniczak, L. and Świtała, M. (2018). Existence and uniqueness results for a time-fractional nonlinear diffusion equation, Journal of Mathematical Analysis and Applications 462(2): 1425-1434.
[28] [28] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego.
[29] [29] Saber Elaydi, S. (2005). An Introduction to Difference Equations, Springer, New York.
[30] [30] Woringer, M., Izeddin, I., Favard, C. and Berry, H. (2020). Anomalous subdiffusion in living cells: Bridging the gap between experiments and realistic models through collaborative challenges, Frontiers in Physics 8(134): 1-9.
[31] [31] Wu, G.C., Baleanu, D., Zeng, S.D. and Deng, Z.G. (2015). Discrete fractional diffusion equation, Nonlinear Dynamics 80(1-2): 281-286.