A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types
Amaç & Hipotez:In this study, we introduce multidelay fractional differential equations with variable coefficients in a uniqueformula.
📊
Temel Bulgular & Veri:A novel graph-operational matrix method based on the fractional Caputo, Riemann–Liouville, Caputo–Fabrizio,and Jumarie derivative types is developed to efficiently solve them.
💡
Sonuç & Katkı:Finally, an illustrative algorithm is presented.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
In this study, we introduce multidelay fractional differential equations with variable coefficients in a uniqueformula. A novel graph-operational matrix method based on the fractional Caputo, Riemann–Liouville, Caputo–Fabrizio,and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points andmatrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractionalderivative types is more appropriate for the method. The solutions of model problems are improved via a new residualerror analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulnessof the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.
🔖
Bu Makaleye Atıf Yap
SEZER, M., KÜRKÇÜ, Ö. K., ASLAN, E. (2022). A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 373–392. https://ajindex.com/articles/607595
Abd-Elhameed WM, Youssri YH. Generalized Lucas polynomial sequence approach for fractional differential equations. Nonlinear Dyn 2017; 89: 1341–1355
Abd-Elhameed WM, Youssri YH. Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations. Comput Appl Math 2018; 37: 2897–2921
Abdulaziz O, Hashim I, Momani S. Application of homotopy-perturbation method to fractional IVPs. J Comput Appl Math 2008; 216: 574-584
Abramowitz M, Stegun IA. Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables. Gaithersburg, MD, USA: National Bureau of Standards, 1964
Aihara J. Matrix representation of an olefinic reference structure for monocyclic conjugated compounds. Bull Chem Soc Japan 1979; 52: 1529-1530
Araujo O, Estrada M, Morales DA, Rada J. The higher-order matching polynomial of a graph. Int J Math Math Sci 2005; 10: 1565-1576
Aslan E. A measure of graphs vulnerability: Edge scattering number. Bull Int Math Virtual Inst 2014; 4: 53-60
Bacak-Turan G, Kırlangıç A. Neighbor rupture degree and the relations between other parameters. Ars Combin 2011; 102: 333-352
Bagley RL, Torvik PJ. On the appearance of the fractional derivative in the behaviour of real materials. J Appl Mech 1984; 51: 294-298
Baleanu D, Mousalou A, Rezapour S. A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative. Adv Differ Equ 2017; 2017: 51
Bhrawy AH, Al-Zahrani AA, Alhamed YA, Baleanu D. A new generalized Laguerre-Gauss collocation scheme for numerical solution of generalized fractional pantograph equations. Rom J Phys 2014; 59: 646-657
Bian H, Zhang F, Wang G, Yu H. Matching polynomials for chains of cycles. Discrete Math 20111; 311: 319-323
Bode HW. Network Analysis and Feedback Amplifier Design. Shanghai, China: Tung Hwa Book Company, 1949
Caputo M. Elasticit‘a e Dissipazione. Bologna, Italy: Zanichelli, 1969
Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Prog Fract Differ Appl 2015; 1: 1-13
Cermá J, Došláb Z, Kisela T. Fractional differential equations with a constant delay: stability and asymptotics of solutions. Appl Math Comput 2017; 298: 336-350
Diethelm K. The Analysis of Fractional Differential Equations. Berlin, Germany: Springer-Verlag, 2010
Doha EH, Bhrawy AH, Ezz-Eldien SS. Efficient Chebyshev spectral m