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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Applications of Short Memory Fractional Differential Equations with Impulses

Discontinuity, Nonlinearity, and Complexity 12(1) (2023) 167--182 | DOI:10.5890/DNC.2023.03.012

Babak Shiri$^1$, Guo-Cheng Wu$^1$, Dumitru Baleanu$^{2,3}$

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Dynamical systems' behavior is sometimes varied with some impulse and sudden changes in process. The dynamics of these systems can not be modeled by previous concepts of derivative or fractional derivatives any longer. The short memory concept is a solution and a better choice for fractional modeling of such processes. We apply short memory fractional differential equations for these systems. We propose collocation methods based on piecewise polynomials to approximate solutions of these equations. We provide various examples to demonstrate the application of the short memory derivative for impulse systems and efficiency of the presented numerical methods.


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