Analytical solutions forfuzzysystem using power series approach
DOI:
https://doi.org/10.24297/jam.v12i8.5973Keywords:
Fuzzy differential equations;Residual power series method;Initial value problems; Strongly generalized differentiabilityAbstract
The aim of the present paper is present a relatively new analytical method, called residual power series (RPS) method, for solving system of fuzzy initial value problems under strongly generalized differentiability. The technique methodology provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. The results reveal that the present simulated method is very effective, straightforward and powerful methodology to solve such fuzzy equations.
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References
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[17] I. Komashynska, M. Al-Smadi, O. Abu Arqub, S. Momani, An efficient analytical method for solving singular initial value problems of nonlinear systems, Applied Mathematics & Information Sciences, 10 (2016), 647-656. http://dx.doi.org/10.18576/amis/100224
[18] K. Moaddy, M. AL-Smadi and I. Hashim, A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method, Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 205207, 1-12. http://dx.doi.org/10.1155/2015/205207
[19] I. Komashynska, M. Al-Smadi, A. Ateiwi and S. Al-Obaidy, Approximate analytical solution by residual power series method for system of Fredholm integral equations, Applied Mathematics and Information Sciences, 10 (2016), 975-985. http://dx.doi.org/10.18576/amis/100315
[20] A. El-Ajou, O. Abu Arqub and M. Al-Smadi, A general form of the generalized Taylor's formula with some applications, Applied Mathematical and Computation, 256 (2015), 851-859. http://dx.doi.org/10.1016/j.amc.2015.01.034
[21] M. Al-Smadi, Solving initial value problems by residual power series method, Theoretical Mathematics and Applications, 3 (2013), 199-210.
[22] O. Abu Arqub, Series solution of fuzzy differential equations under strongly generalized differentiability, Journal of Advanced Research in Applied Mathematics, 5 (2013), 31-52.
[23] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems,24 (1987), 301-317. http://dx.doi.org/10.1016/0165-0114(87)90029-7
[24] M.L. Puri, Fuzzy random variables, Journal of Mathematical Analysis and Applications, 114 (1986), 409-422. http://dx.doi.org/10.1016/0022-247x(86)90093-4
http://dx.doi.org/10.1016/j.fss.2011.05.012
[2] R. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems,18 (1986), 31-43. http://dx.doi.org/10.1016/0165-0114(86)90026-6
[3] D.H. Ackley, G.E. Hinton and T.J. Sejnowski, A learning algorithm for Boltzmann machine, Cognitive Science, 9 (1985), 147-169. http://dx.doi.org/10.1016/s0364-0213(85)80012-4
[4] A. Khastan, F. Bahrami, K. Ivaz, New Results on multiple solutions for Nth-order fuzzy differential equations under generalized differentiability, Boundary Value Problems, 2009 (2009), Article ID 395714, 1-13.
http://dx.doi.org/10.1155/2009/395714
[5] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, Numerical Solutions of Fuzzy Differential Equations using Reproducing Kernel Hilbert Space Method, Soft Computing, 2015 (2015), 1-20. http://dx.doi.org/10.1007/s00500-015-1707-4
[6] O. Abu Arqub, Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations, Neural Computing and Applications, 2015 (2015), 1-20. http://dx.doi.org/10.1007/s00521-015-2110-x
[7] G. Gumah, K. Moaddy, M. AL-Smadi and I. Hashim, Solutions of Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method, Journal of Function Spaces, 2016 (2016), Article ID 2920463, 1-11. http://dx.doi.org/10.1155/2016/2920463
[8] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems, Soft Computing, 2016 (2016), 1-16. doi:10.1007/s00500-016-2262-3
[9] R. Saadeh, M. Al-Smadi, G. Gumah, H. Khalil and R.A. Khan, Numerical Investigation for Solving Two-Point Fuzzy Boundary Value Problems by Reproducing Kernel Approach, Applied Mathematics and Information Sciences, 10 (2016), no. 6, 1-13.
[10] I. Komashynska and M. Al-Smadi, Iterative reproducing kernel method for solving second-order integrodifferential equations of Fredholm Type, Journal of Applied Mathematics, 2014 (2014), Article ID 459509, 1-11. http://dx.doi.org/10.1155/2014/459509
[11] M. Al-Smadi, O. Abu Arqub and A. El-Ajou, A numerical iterative method for solving systems of first-order periodic boundary value problems, Journal of Applied Mathematics, 2014 (2014), Article ID 135465, 1-10. http://dx.doi.org/10.1155/2014/135465
[12] O. Abu Arqub, M. Al-Smadi and S. Momani, Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integrodifferential equations, Abstract and Applied Analysis, 2012 (2012), Article ID 839836, 1-16. http://dx.doi.org/10.1155/2012/839836
[13] O. Abu Arqub and M. Al-Smadi, Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations, Applied Mathematical and Computation, 243 (2014), 911-922. http://dx.doi.org/10.1016/j.amc.2014.06.063
[14] M. Al-Smadi, O. Abu Arqub and S. Momani, A Computational Method for Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential Equations, Mathematical Problems in Engineering, 2013 (2013), Article ID 832074, 1-10. http://dx.doi.org/10.1155/2013/832074
[15] O. Abu Arqub, M. Al-Smadi and N. Shawagfeh, Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method, Applied Mathematics and Computation, 219 (2013), 8938-8948. http://dx.doi.org/10.1016/j.amc.2013.03.006
[16] M. Al-Smadi, O. Abu Arqub, N. Shawagfeh and S. Momani, Numerical investigations for systems of secondorder periodic boundary value problems using reproducing kernel method, Applied Mathematical and Computation, 291 (2016), 137-148. http://dx.doi.org/10.1016/j.amc.2016.06.002
[17] I. Komashynska, M. Al-Smadi, O. Abu Arqub, S. Momani, An efficient analytical method for solving singular initial value problems of nonlinear systems, Applied Mathematics & Information Sciences, 10 (2016), 647-656. http://dx.doi.org/10.18576/amis/100224
[18] K. Moaddy, M. AL-Smadi and I. Hashim, A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method, Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 205207, 1-12. http://dx.doi.org/10.1155/2015/205207
[19] I. Komashynska, M. Al-Smadi, A. Ateiwi and S. Al-Obaidy, Approximate analytical solution by residual power series method for system of Fredholm integral equations, Applied Mathematics and Information Sciences, 10 (2016), 975-985. http://dx.doi.org/10.18576/amis/100315
[20] A. El-Ajou, O. Abu Arqub and M. Al-Smadi, A general form of the generalized Taylor's formula with some applications, Applied Mathematical and Computation, 256 (2015), 851-859. http://dx.doi.org/10.1016/j.amc.2015.01.034
[21] M. Al-Smadi, Solving initial value problems by residual power series method, Theoretical Mathematics and Applications, 3 (2013), 199-210.
[22] O. Abu Arqub, Series solution of fuzzy differential equations under strongly generalized differentiability, Journal of Advanced Research in Applied Mathematics, 5 (2013), 31-52.
[23] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems,24 (1987), 301-317. http://dx.doi.org/10.1016/0165-0114(87)90029-7
[24] M.L. Puri, Fuzzy random variables, Journal of Mathematical Analysis and Applications, 114 (1986), 409-422. http://dx.doi.org/10.1016/0022-247x(86)90093-4
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Published
2016-09-15
How to Cite
Abughurra, S. (2016). Analytical solutions forfuzzysystem using power series approach. JOURNAL OF ADVANCES IN MATHEMATICS, 12(8), 6553–6559. https://doi.org/10.24297/jam.v12i8.5973
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