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Keywords: Caputo derivative
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Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. December 2024, 19(12): 121008.
Paper No: CND-23-1350
Published Online: October 18, 2024
...:  odibat@bau.edu.jo ; z.odibat@gmail.com fractional calculus fractional differential equation Caputo derivative Mittag-Leffler kernel cardinal sine kernel convergent series singular kernel Proof 5 . From Definition 4, we have (40) ∫ 0 a | M D k α α...
Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. December 2024, 19(12): 121002.
Paper No: CND-24-1038
Published Online: September 21, 2024
... = 0 where 0 < μ ≤ 1 , and ∂ μ v ∂ t μ : = D t μ v represents the Caputo derivative. In the system ( 1.2 ), the fractional derivatives “remember” the past states of the water waves. This means the current state of the wave (e.g...
Journal Articles
Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. January 2024, 19(1): 011001.
Paper No: CND-22-1328
Published Online: October 26, 2023
.... In Ref. [ 43 ], Zhao et al. studied anomalous diffusion and wave propagation models and derived two second-order approximation formulas for the Caputo derivative of variable order. There are some works on the second-order approximation for the Caputo derivative that use the adaptive time-stepping...
Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. October 2023, 18(10): 101003.
Paper No: CND-22-1295
Published Online: July 26, 2023
... and does not include any tedious calculations. Moreover, it is easily employable using the computer algebra system such as Mathematica, Maple, etc. 1 Corresponding author. e-mail:  mkmath14@gmail.com 26 10 2022 17 06 2023 26 07 2023 Caputo derivative fractional PDEs...
Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. September 2023, 18(9): 091007.
Paper No: CND-22-1149
Published Online: July 12, 2023
... of simulating related fractional models. 1 Corresponding author. e-mails:  odibat@bau.edu.jo ; z.odibat@gmail.com 08 06 2022 05 06 2023 12 07 2023 Caputo derivative Mittag-Leffler kernel fractional differential equation predictor–corrector algorithm Fractional...
Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. February 2023, 18(2): 021001.
Paper No: CND-21-1340
Published Online: December 9, 2022
... ; z.odibat@gmail.com 26 10 2021 02 11 2022 09 12 2022 optimized decomposition method linear approximation Adomian decomposition method Caputo derivative fractional differential equation The topic of fractional calculus has received great popularity and importance over...
Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. January 2023, 18(1): 011006.
Paper No: CND-21-1250
Published Online: November 21, 2022
...–Baleanu senses. The population dynamics model, which includes the predator-prey equation and the logistic equation, is generalized by employing a fractional operator based on the Caputo–Fabrizio derivative [ 9 ]. Reference [ 10 ] presented the fractional Burgess equations in terms of Caputo derivative...
Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. March 2015, 10(2): 021019.
Paper No: CND-14-1030
Published Online: March 1, 2015
... reaction subdiffusion equation Neumann boundary conditions operational matrix Tau-spectral method Riemann–Liouville integral Caputo derivative In recent decades, fractional differential equations (FDEs) (differential equations with noninteger arbitrary order) have gained much attention...
Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. April 2013, 8(2): 021011.
Paper No: CND-12-1068
Published Online: August 31, 2012
... equations we conclude that our method gave comparable results. fractional calculus 0perational matrix Legendre polynomials Caputo derivative tau method Fractional calculus is an emerging field both in the theoretical and applied aspects [ 1–18 ]. During the last decades, several methods...