Browsing by Author "Wu, G.-C."

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Citation - Scopus: 20
Applications of Short Memory Fractional Differential Equations With Impulses
(L and H Scientific Publishing, LLC, 2023) Wu, G.-C.; Baleanu, D.; Shiri, B.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. © 2023 L&H Scientific Publishing, LLC. All rights reserved
Citation - Scopus: 5
Chaos Synchronization of the Fractional Rucklidge System Based on New Adomian Polynomials
(L and H Scientific Publishing, LLC, 2017) Baleanu, D.; Huang, L.-L.; Wu, G.-C.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The fractional Rucklidge system is a new kind of chaotic models which hold the feature of memory effects and can depict the long history interactions. A numerical formula is proposed by use of the fast Adomian polynomials. Chaotic behavior are discussed and the Poincare sections are given for various fractional cases. It's also applied in chaos synchronization of the fractional system. © 2017 L & H Scientific Publishing, LLC.
Citation - Scopus: 14
Discrete Fractional Masks and Their Applications To Image Enhancement
(De Gruyter, 2019) Baleanu, D.; Bai, Y.-R.; Wu, G.-C.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Fractional differences for image enhancement are revisited and the general methodology is illustrated in this chapter. Several fractional differences are theoretically analyzed and numerically compared. The weight coefficients derived from the discrete fractional calculus are a set of conserved quantities and they are suitable for image processing. Then a discrete fractional mask is designed within the Caputo difference and the mask coefficients are given by use of the Gamma functions. In comparison with the Grünwald-Letnikov difference and Riemann-Liouville masks, the results show this novel mask’s efficiency and simplicity. © 2019 Walter de Gruyter GmbH, Berlin/Boston.
Recent Theory and Applications on Numerical Algorithms and Special Functions
(Hindawi Publishing Corporation, 2015) Van Gorder, R.A.; Baleanu, D.; Wu, G.-C.; Bhrawy, A.H.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - Scopus: 14
Several Fractional Differences and Their Applications To Discrete Maps
(L and H Scientific Publishing, LLC, 2015) Baleanu, D.; Zeng, S.-D.; Wu, G.-C.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Several definitions of fractional differences are discussed. Their applications to fractional maps are compared. As an example, the logistic equation of integer order is discretized by these fractional difference methods. The comparative results show that the discrete fractional calculus is an efficient tool and the maps derived in this way have simpler forms but hold rich dynamical behaviors. © 2015 L & H Scientific Publishing, LLC.