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Fractional B-spline collection method for solving fractal-differential equations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، Special Issue، اسفند 2021، صفحه 745-754 اصل مقاله (475.91 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5428 | ||
| نویسندگان | ||
| Aml M. Shloof1؛ Aisha Gewily* 2 | ||
| 1Department of Mathematics, Faculty of Science, Al-Zintan University, Libya | ||
| 2Faculty of Arts and Science Al-Wahat, Benghazi University, Libya | ||
| تاریخ دریافت: 10 تیر 1399، تاریخ پذیرش: 03 دی 1399 | ||
| چکیده | ||
| This study used the fractional B-spline collocation technique to obtain the numerical solution of fractal-fractional differential equations. The technique was considered to solve the fractal-fractional differential equations (FFDEs) with ($0 <\gamma_i < 1,\, i = 1, 2, \cdots, N$). In this suggested technique, the B-spline of fractional order was utilised in the collocation technique. The scheme was easily attained, efficient, and relatively precise with reduced computational work numerical findings. Via the proposed technique, FFDEs can be reduced for solving a system of linear algebraic equations using an appropriate numerical approach. The verified numerical illustrative experiments were presented will show the effectiveness of the technique proposed in this study in solving FFDEs in three cases of nonlocal integral and differential operators namely power law kernel, when the kernels are exponential and the generalization of Mittag-Leffler kernel. The approximate solution is very good and accurate to the exact solution. | ||
| کلیدواژه‌ها | ||
| fractional B-spline؛ Linear fractional differential equations FDEs؛ Caputo-Fabrizio derivative C-F | ||
| مراجع | ||
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[1] A. Alsaedi, J. , Nieto and V. Venktesh, Fractional electrical circuits , Adv. Mech. Eng. 7(12) (2015) 1–7. [2] I. Area, F. Batarfi, J. Losada, J. Nieto, W. Shammakh and A. Torres, On a fractional order Ebola epidemic model, Adv. Diff. Equ, 2015 (2015) 278. [3] A. Atangana, Fractal-fractional differentiation and integration:connecting fractal calculus and fractional calculus to predict complex, system, Chaos Solitons Fract. 102 (2017) 396-–406. [4] A. Atangana, Blind in a commutative world: simple illustrations with functions and chaotic attractors, Chaos Solitons Fract. 114 (2018) 347—363. [5] A. Atangana and J. Aguilar, Decolonisation of fractional calculus rules: breaking commutativity and associativity to capture more natural phenomena, Eur. Phys. J. Plus. 133(4) (2018) 166, . [6] A. Atangana, A. Akgul and K. Owolabi, Analysis of fractal fractional differential equations, Alexandria Engin. J. 59(3) (2020) 1117–1134. [7] A. Atangana and B. Alkahtani, Analysis of the Keller–Segel model with a fractional derivative without singular kernel, SIAM J. Numerical Anal. 17(6) (2015) 4439—4453. [8] A. Atangana and S. Jain,A new numerical approximation of the fractal ordinary differential, Euro. Phys. J. Plus. 133(37) (2018). [9] I. Azhar, J. Mohd, M. Imad and M. Muhammad, Nonlinear waves propagation and stability analysis for planar waves at far field using quintic B-spline collocation method, Alexandria Engin. J. 59(4) (2020) 2695–2703. [10] A. Blu and M. Unser, The fractional spline wavelet transform: defnition and implementation, Proc. Twenty-Fifth IEEE Int. Conf. Acoust. Speech Signal Proces. 2000, pp. 512–515. [11] M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Diff. Appl. 1(2) (2015) 1-–13. [12] K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer, Berlin, 2010. [13] P. Francesca, A fractional B-spline collection method for the numerical solution of fractional Predator-Prey models Fract. Fract. 1(16), (2018). [14] T. In´es, P. Emiliano and V. Duarte, Fractional derivatives for economic growth modelling of the group of twenty: Application to prediction, Math. 8(1) (2020) 50. [15] H. Jafari, C. Khalique, M. Ramezani and H. Tajadodi, Numerical solution of fractional differential equations by using fractional B-spline, Open Phys. 11(10) (2013) 1372–1376. [16] A. Kilbas, M. Srivastava and J. Trujillo, Theory and Applications of Fractional Differential Equations, NorthHolland, Amsterdam, 2006. [17] D. Kumar, J. Singh, M. Al Qurashi and D. Baleanu, Analysis of logistic equation pertaining to a new fractional derivative with non-singular kernel, Adv. Mech. Eng. 9(2) (2017). [18] D. Kumar, J. Singh and D. Baleanu, Numerical computation of a fractional model of differential-difference equation, J. Comput. Nonlinear Dyn. 11(6) (2014) 061004. [19] D. Kumar, F. Tchier, F. Singh and D. Baleanu An efficient computational technique for fractal vehicular traffic flow, Entropy 20(4) (2018). [20] J. Losada and J.J. Nieto, Properties of a new fractional derivative without singular kernel, Prog. Fract. Differ. Appl. 1(2) (2015) 87–92. [21] M. Ma, D. Baleanu, Y. Gasimov and J. Yang, New results for multidimensional diffusion equations in fractal dimensional space,Rom. J. Phys. 61 (2016) 784—794. [22] F. Mainardi, Fractional calculus: some basic problems in continuum and statistical mechanics, Springer, Wien, 1997. [23] Z. Meng, M. Yi and J. Huang J, L. Song, Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials, Appl Math Comput. 336 (2018) 454–464. [24] M. Owolabi and A. Atangana, Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative, Chaos Solitons Fract. 105 (2017) 111—119. [25] I. Podlubny, Fractional Diferential Equations, Academic, San Diego, 1999.[26] M. Ramezani, Numerical analysis nonlinear multi-term time fractional differential equation with collection method via fractional B-spline, Math. Meth. Appl. Sci.(42) (2015) 4640–4663. [27] M. Ramezani, H. Jafari , S. Johnson and D. Baleanu, Complex B-spline collocation method for solvingweakly singularVolterra integral equations of the second kind, Miskolc Math. Notes 16(2) (2015) 1091–1103. [28] J. Singh, D. Kumar and D. Baleanu, New aspects of fractional Biswas–Milovic model with Mittag–Leffler law, Math. Model. Nat. Phenom. 14(3) (2019) 303. [29] A. Tateishi, H. , Ribeiro and E. Lenzi, The role of fractional time-derivative operators on anomalous diffusion, Front. Phys. 5(52) (2017). [30] M. Unser and T. Blu, Fractional splines and wavelets, SIAM Rev. 42(1) (2000) 43–67. | ||
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