An optimization method for solving fractional oscillation equation
This paper seeks to present an optimization method to estimate the solutions of nonlinear oscillation equations of fractional order. The mentioned method is based on Bernstein polynomials (Bps). In the presented numerical approach, the operational matrices of the ordinary and fractional derivatives...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-02-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379724000858 |
| _version_ | 1827349857249001472 |
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| author | Haleh Tajadodi Hasib Khan Jehad Alzabut J.F. Gómez-Aguilar |
| author_facet | Haleh Tajadodi Hasib Khan Jehad Alzabut J.F. Gómez-Aguilar |
| author_sort | Haleh Tajadodi |
| collection | DOAJ |
| description | This paper seeks to present an optimization method to estimate the solutions of nonlinear oscillation equations of fractional order. The mentioned method is based on Bernstein polynomials (Bps). In the presented numerical approach, the operational matrices of the ordinary and fractional derivatives of Bernstein polynomials are utilized to estimate the solution of the model under the study. In this technique, the unknown function is expanded in terms of Bps. By using the residual function and its 2-norm, the problem under consideration is converted into a constrained nonlinear optimization one. So that, the constraint equations are obtained from the given initial conditions and the object function is obtained from the residual function. Finally, we obtain the unknown coefficients optimally by a set of unknown Lagrange multipliers. The main advantage of this approach is that it reduces such problems to those optimization problems, which greatly simplifies them and also leads to obtain a good approximate solution for them. The accuracy and efficiency of the presented method are supported by some examples. At the end, we compare the numerical results with other results. |
| first_indexed | 2024-03-08T00:50:17Z |
| format | Article |
| id | doaj.art-bdb22f5d8483492fbacac07ce55b54d1 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-08T00:50:17Z |
| publishDate | 2024-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-bdb22f5d8483492fbacac07ce55b54d12024-02-15T05:23:54ZengElsevierResults in Physics2211-37972024-02-0157107403An optimization method for solving fractional oscillation equationHaleh Tajadodi0Hasib Khan1Jehad Alzabut2J.F. Gómez-Aguilar3Department of Mathematics, University of Sistan and Baluchestan, Zahedan, IranDepartment of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia; Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia; Department of Industrial Engineering, OSTIM Technical University, 06374 Ankara, TurkiyeCentro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp-IICBA)/UAEM, Universidad Autónoma del Estado de Morelos. Av. Universidad 1001 Col. Chamilpa, C.P. 62209 Cuernavaca, Morelos, Mexico; Universidad Tecnológica de México, UNITEC MÉXICO-Campus En Línea, Mexico, Mexico; Corresponding author at: Centro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp-IICBA)/UAEM, Universidad Autónoma del Estado de Morelos. Av. Universidad 1001 Col. Chamilpa, C.P. 62209 Cuernavaca, Morelos, Mexico.This paper seeks to present an optimization method to estimate the solutions of nonlinear oscillation equations of fractional order. The mentioned method is based on Bernstein polynomials (Bps). In the presented numerical approach, the operational matrices of the ordinary and fractional derivatives of Bernstein polynomials are utilized to estimate the solution of the model under the study. In this technique, the unknown function is expanded in terms of Bps. By using the residual function and its 2-norm, the problem under consideration is converted into a constrained nonlinear optimization one. So that, the constraint equations are obtained from the given initial conditions and the object function is obtained from the residual function. Finally, we obtain the unknown coefficients optimally by a set of unknown Lagrange multipliers. The main advantage of this approach is that it reduces such problems to those optimization problems, which greatly simplifies them and also leads to obtain a good approximate solution for them. The accuracy and efficiency of the presented method are supported by some examples. At the end, we compare the numerical results with other results.http://www.sciencedirect.com/science/article/pii/S2211379724000858Optimization methodOperational matrixOscillation equationsBernstein polynomials |
| spellingShingle | Haleh Tajadodi Hasib Khan Jehad Alzabut J.F. Gómez-Aguilar An optimization method for solving fractional oscillation equation Results in Physics Optimization method Operational matrix Oscillation equations Bernstein polynomials |
| title | An optimization method for solving fractional oscillation equation |
| title_full | An optimization method for solving fractional oscillation equation |
| title_fullStr | An optimization method for solving fractional oscillation equation |
| title_full_unstemmed | An optimization method for solving fractional oscillation equation |
| title_short | An optimization method for solving fractional oscillation equation |
| title_sort | optimization method for solving fractional oscillation equation |
| topic | Optimization method Operational matrix Oscillation equations Bernstein polynomials |
| url | http://www.sciencedirect.com/science/article/pii/S2211379724000858 |
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