References
- Alaroud, M., Aljarrah, H., Alomari, A.-K., Ishak, A. and Darus, M. (2024). Explicit and approximate series solutions for nonlinear fractional wave-like differential equations with variable coefficients, Partial Differential Equations in Applied Mathematics 10: 100680.
- Bekir, A., Aksoy, E. and Cevikel, A.C. (2015). Exact solutions of nonlinear time fractional partial differential equations by sub-equation method, Mathematical Methods in the Applied Sciences 38(13): 2779–2784.
- Blaszczyk, T., Bekus, K., Szajek, K. and Sumelka, W. (2021). On numerical approximation of the Riesz–Caputo operator with the fixed/short memory length, Journal of King Saud University-Science 33(1): 101220.
- Chechkin, A.V., Seno, F., Metzler, R. and Sokolov, I.M. (2017). Brownian yet non-Gaussian diffusion: From superstatistics to subordination of diffusing diffusivities, Physical Review X 7: 021002.
- Ciesielski, M. and Leszczynski, J. (2006). Numerical treatment of an initial-boundary value problem for fractional partial differential equations, Signal Processing 86(10): 2619–2631.
- Das, S. (2009). Analytical solution of a fractional diffusion equation by variational iteration method, Computers & Mathematics with Applications 57(3): 483–487.
- dos Santos, M.A. (2019). Analytic approaches of the anomalous diffusion: A review, Chaos, Solitons & Fractals 124: 86–96.
- Echchaffani, Z., Aberqi, A., Karite, T. and Leiva, H. (2024). The existence of mild solutions and approximate controllability for nonlinear fractional neutral evolution systems, International Journal of Applied Mathematics and Computer Science 34(1): 15–2.
- Elkott, I., Latif, M.S.A., El-Kalla, I.L. and Kader, A.H.A. (2023). Some closed form series solutions for the time-fractional diffusion-wave equation in polar coordinates with a generalized Caputo fractional derivative, Journal of Applied Mathematics and Computational Mechanics 22(2): 5–14.
- Evangelista, L.R. and Lenzi, E.K. (2018). Fractional Diffusion Equations and Anomalous Diffusion, Cambridge University Press, Cambridge.
- Gu, X.-M., Sun, H.-W., Zhao, Y.-L. and Zheng, X. (2021). An implicit difference scheme for time-fractional diffusion equations with a time-invariant type variable order, Applied Mathematics Letters 120: 107270.
- Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.
- Klimek, M. and Blaszczyk, T. (2024). Exact solutions of fractional oscillator eigenfunction problem with fixed memory length, Journal of Applied Mathematics and Computational Mechanics 23(1): 45–58.
- Ledesma, C.T., Baca, J.V. and Sousa, J.V.d.C. (2022). Properties of fractional operators with fixed memory length, Mathematical Methods in the Applied Sciences 45(1): 49–76.
- Ledesma, C.T., Rodríguez, J.A. and Sousa, J.V.d.C. (2023). Differential equations with fractional derivatives with fixed memory length, Rendiconti del Circolo Matematico di Palermo Series 2 72(1): 635–653.
- Lu, Z. and Fan, W. (2025). A fast algorithm for multi-term time-space fractional diffusion equation with fractional boundary condition, Numerical Algorithms 98: 1171–1194.
- Magin, R.L. (2006). Fractional Calculus in Bioengineering, Begell House Publisher, Danbury.
- Magin, R.L., Abdullah, O., Baleanu, D. and Zhou, X.J. (2008). Anomalous diffusion expressed through fractional order differential operators in the bloch-torrey equation, Journal of Magnetic Resonance 190(2): 255–270.
- Malinowska, A.B., Odzijewicz, T. and Poskrobko, A. (2023). Applications of the fractional Sturm–Liouville difference problem to the fractional diffusion difference equation, International Journal of Applied Mathematics and Computer Science 33(3): 349–359, DOI: 10.34768/amcs-2023-0025.
- Meerschaert, M.M. and Tadjeran, C. (2004). Finite difference approximations for fractional advection-dispersion flow equations, Journal of Computational and Applied Mathematics 172(1): 65–77.
- Metzler, R. and Klafter, J. (2000). The random walk’s guide to anomalous diffusion: A fractional dynamics approach, Physics Reports 339(1): 1–77.
- Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego.
- Stempin, P., Pawlak, T.P. and Sumelka, W. (2023). Formulation of non-local space-fractional plate model and validation for composite micro-plates, International Journal of Engineering Science 192: 103932.
- Sumelka, W., Blaszczyk, T. and Liebold, C. (2015). Fractional euler-bernoulli beams: Theory, numerical study and experimental validation, European Journal of Mechanics A/Solids 54: 243–251.
- Sumelka, W., Łuczak, B., Gajewski, T. and Voyiadjis, G.Z. (2020). Modelling of AAA in the framework of time-fractional damage hyperelasticity, International Journal of Solids and Structures 206: 30–42.
- Tian, W., Zhou, H. and Deng, W. (2015). A class of second order difference approximations for solving space fractional diffusion equations, Mathematics of Computation 84(294): 1703–1727.
- Tsallis, C. and Lenzi, E. (2002). Anomalous diffusion: Nonlinear fractional Fokker–Planck equation, Chemical Physics 284(1): 341–347.
- Voyiadjis, G., Akbari, E., Łuczak, B. and Sumelka, W. (2023). Towards determining an engineering stress-strain curve and damage of the cylindrical lithium-ion battery using the cylindrical indentation test, Batteries 9(4): 233.
- Wang, H. and Du, N. (2013). A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations, Journal of Computational Physics 240: 49–57.
- Wei, Y., Chen, Y., Cheng, S. and Wang, Y. (2017). A note on short memory principle of fractional calculus, Fractional Calculus and Applied Analysis 20(6): 1382–1404.
- Yang, X., Wu, L. and Zhang, H. (2023). A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity, Applied Mathematics and Computation 457: 128192.
- Zaslavsky, G.M. (2000). Chaos, fractional kinetics, and anomalous transport, Physics Reports 371(6): 461–580.
- Zhuang, P., Liu, F., Turner, I. and Anh, V. (2016). Galerkin finite element method and error analysis for the fractional cable equation, Numerical Algorithms 72: 447–466.