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The approximate analytical solutions of nonlinear fractional ordinary differential equations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 527-535 اصل مقاله (349.49 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5094 | ||
| نویسندگان | ||
| Lamees K. Alzaki* 1؛ Hassan Kamil Jassim2 | ||
| 1Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| 2Department of Mathematics, University of Thi-Qar, Nasiriyah, Iraq | ||
| تاریخ دریافت: 16 بهمن 1399، تاریخ بازنگری: 29 فروردین 1400، تاریخ پذیرش: 21 اردیبهشت 1400 | ||
| چکیده | ||
| The Sumudu homotopy perturbation method (SHPM) is applied to solve fractional order nonlinear differential equations in this paper.The current technique incorporates two notable strategies in particular Sumudu transform (ST) and homotopy perturbation method (HPM). The proposed method’s hybrid property decreases the number of the quantity of computations and materials needed. In this method, illustration examples evaluate the accuracy and applicability of the mentioned procedure. The outcomes got by FSHPM are in acceptable concurrence with the specific arrangement of the problem. | ||
| کلیدواژهها | ||
| Homotopy perturbation method؛ fractional differential equation؛ sumudu transform, Caputo fractional derivative | ||
| مراجع | ||
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[1] I. Podlubny,Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, San Diego, California, USA, 1999. [2] A. A. Kilbas, H. M. Srivastava, J. T. Juan, Theory and applications of fractional differential equations, NorthHolland, Jan Van Mill (2006). [3] R. Hilfer, Applications of fractional calculus in physics, Singapore, Word Scientific Company, (2000). [4] I. Petras,Fractional-order nonlinear systems: modeling, analysis and simulation, Beijing, Higher Education Press, (2011).[5] H. K. Jassim, J. Vahidi,A new technique of reduce differential transform method to solve local fractional PDEs in mathematical physics, International Journal of Nonlinear Analysis and Applications, 12(1) (2021) 37-44. [6] W. H. Su, D. Baleanu, et al. Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method, Fixed Point Theory and Applications, 2013 (2013) 1-11. [7] H. Jafari, H. K. Jassim, Local fractional variational iteration method for nonlinear partial differential equations within local fractional operators, Applications and Applied Mathematics, 10 (2015) 1055-1065. [8] X. J. Yang,Local fractional functional analysis and its applications, Asian Academic, Hong Kong, China, (2011). [9] S. Xu, X. Ling, Y. Zhao, H. K. Jassim,A novel schedule for solving the two-dimensional diffusion in fractal heat transfer, Thermal Science, 19 (2015) S99-S103. [10] H. K. Jassim, W.A. Shahab, Fractional variational iteration method to solve one dimensional second order hyperbolic telegraph equations, Journal of Physics: Conference Series, 1032(1) (2018) 1-9. [11] X. J. Yang, J. A. Machad, H. M. Srivastava, A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach, Applied Mathematics and Computation, 274 (2016) 143-151. [12] H. Jafari, H. K. Jassim, F. Tchier, D. Baleanu, On the approximate solutions of local fractional differential equations with local fractional operator, Entropy, 18 (2016). [13] H. K. Jassim, J. Vahidi, V. M. Ariyan, Solving Laplace equation within local fractional operators by using local fractional differential transform and Laplace variational iteration methods, Nonlinear Dynamics and Systems Theory, 20(4) (2020) 388-396. [14] A. M. Yang, et al. Local fractional series expansion method for solving wave and diffusion equations Cantor sets, Abstract and Applied Analysis, 2013 (2013) 1-5. [15] H. K. Jassim, D. Baleanu, A novel approach for Korteweg-de Vries equation of fractional order, Journal of Applied Computational Mechanics, 5(2) (2019) 192-198. [16] H. K. Jassim, S. A. Khafif,SVIM for solving Burger’s and coupled Burger’s equations of fractional order, Progress in Fractional Differentiation and Applications, 7(1) (2021). [17] H. A. Eaued, H. K. Jassim, M. G. Mohammed,A novel method for the analytical solution of partial differential equations arising in mathematical physics, IOP Conf. Series: Materials Science and Engineering, 928 (042037) (2020) 1-16. [18] C. G. Zhao, et al., The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative, Abstract and Applied Analysis, 2014 (2014) 1-5. [19] Y. Zhang, X. J. Yang, and C. Cattani, Local fractional homotopy perturbation method for solving nonhomogeneous heat conduction equations in fractal domain, Entropy, 17 (2015) 6753-6764. [20] H. K. Jassim, M. A. Shareef,On approximate solutions for fractional system of differential equations with CaputoFabrizio fractional operator, Journal of Mathematics and Computer science, 23 (2021) 58-66. [21] H. K. Jassim, H. A. Kadhim, Fractional Sumudu decomposition method for solving PDEs of fractional order, Journal of Applied and Computational Mechanics, 7(1) (2021) 302-311. [22] D. Baleanu, H.K. Jassim,Exact Solution of Two-dimensional Fractional Partial Differential Equations, Fractal Fractional, 4(21) (2020) 1-9. [23] M. S. Hu, et al. Local fractional Fourier series with application to wave equation in fractal vibrating, Abstract and Applied Analysis, 2012 (2012) 1-7. [24] H. Jafari, et al.,Reduced differential transform method for partial differential equations within local fractional derivative operators, Advances in Mechanical Engineering, 8(4) (2016) 1-6. [25] H. Jafari, H. K. Jassim, J. Vahidi, Reduced differential transform and variational iteration methods for 3d diffusion model in fractal heat transfer within local fractional operators, Thermal Science, 22(2018) S301-S307. [26] J. Singh, H.K. Jassim, D. Kumar, An efficient computational technique for local fractional Fokker-Planck equation, Physica A: Statistical Mechanics and its Applications, 555(124525) (2020) 1-8. [27] Z. P. Fan, H. K. Jassim, R. K. Rainna, and X. J. Yang,Adomian Decomposition Method for Three-Dimensional Diffusion Model in Fractal Heat Transfer Involving Local Fractional Derivatives, Thermal Science, 19(2015) S137- S141. [28] S. P. Yan, H. Jafari, and H. K. Jassim, Local fractional Adomian decomposition and function decomposition methods for solving Laplace equation within local fractional operators, Advances in Mathematical Physics, 2014 (2014) 1-7. [29] D. Baleanu, H. K. Jassim, Approximate Analytical Solutions of Goursat Problem within Local Fractional Operators, Journal of Nonlinear Science and Applications, 9(2016) 4829-4837. [30] H. K. Jassim, Analytical Approximate Solutions for Local Fractional Wave Equations, Mathematical Methods in the Applied Sciences, 43(2) (2020) 939-947. [31] D. Baleanu, D. Baleanu, H. K. Jassim, A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets, Fractal and Fractional, 3(30) (2019) 1-8. [32] D. Baleanu, H. K. Jassim, M. Al Qurashi, Solving Helmholtz Equation with Local Fractional Derivative Operators, Fractal and Fractional, 3(43) (2019) 1-13. [33] H. Jafari, H. K. Jassim, D. Baleanu, Y. M. Chu, On the approximate solutions for a system of coupled Korteweg-de Vries equations with local fractional derivative, Fractals, 29(5)(2021) 1-7. [34] D. Baleanu, H. K. Jassim, Approximate Solutions of the Damped Wave Equation and Dissipative Wave Equationin Fractal Strings, Fractal and Fractional, 3(26) (2019) 1-12. [35] H. K. Jassim, C. Unl¨u, S. P. Moshokoa, C. M. Khalique, ¨ Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering, 2015 (2015) 1-7. [36] D. Baleanu, H.K. Jassim, A Modification Fractional Variational Iteration Method for solving Nonlinear Gas Dynamic and Coupled KdV Equations Involving Local Fractional Operators, Thermal Science, 22(2018) S165- S175. [37] S. M. Kadhim, M. G. Mohammad, H. K. Jassim, How to Obtain Lie Point Symmetries of PDEs, Journal of Mathematics and Computer science, 22 (2021) 306-324. [38] H. K. Jassim, M. G. Mohammed,Natural homotopy perturbation method for solving nonlinear fractional gas dynamics equations, International Journal of Nonlinear Analysis and Applications, 12(1) (2021) 37-44. [39] H. K. Jassim, The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator, Abstract and Applied Analysis, 2016 (2016) 1-5. [40] M. G. Mohammed, H. K. Jassim, Numerical simulation of arterial pulse propagation using autonomous models, International Journal of Nonlinear Analysis and Applications, 12(1) (2021) 841-849. [41] H. K. Jassim, A new approach to find approximate solutions of Burger’s and coupled Burger’s equations of fractional order, TWMS Journal of Applied and Engineering Mathematics, 11(2) (2021) 415-423. [42] H. K. Jassim, On Approximate Methods for Fractal Vehicular Traffic Flow, TWMS Journal of Applied and Engineering Mathematics, 7(1) (2017) 58-65. [43] H. K. Jassim, A Novel Approach for Solving Volterra Integral Equations Involving Local Fractional Operator, Applications and Applied Mathematics, 12(1) (2017) 496 – 505. [44] H. Jafari, H. K. Jassim, Application of Local Fractional Variational Iteration Method to Solve System of Coupled Partial Differential Equations Involving Local Fractional Operator, Applied Mathematics and Information Sciences Letters, 5(2) (2017) 1-6. [45] H. K. Jassim,The Analytical Solutions for Volterra Integro-Differential Equations Involving Local Fractional Operators by Yang-Laplace Transform, Sahand Communications in Mathematical Analysis, 6 (1) (2017) 69-76. [46] H. Jafari, H. K. Jassim, A new approach for solving a system of local fractional partial differential equations, Applications and Applied Mathematics, 11(1) (2016) 162-173. [47] Z. Odibat and S. Momani, Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order, Chaos, Solitons and Fractals, 36(1) (2008) 167–174. | ||
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