Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Publicado
New results regarding the existence, uniqueness and convergence of the solution for nonlinear fractional Volterra integro-differential equations via Caputo-Fabrizio operator
Nuevos resultados sobre la existencia, unicidad y convergencia de la solución para ecuaciones integro-diferenciales fraccionarias no lineales de Volterra mediante el operador Caputo-Fabrizio
DOI:
https://doi.org/10.15446/recolma.v58n1.117441Palabras clave:
Fractional Volterra integro-differential equations, Caputo- Fabrizio fractional operator, Banach contraction principle, Khalouta transform method, Adomian decomposition method (en)Ecuaciones diferenciales integro-fraccionales de Volterra, operador fraccionario de Caputo-Fabrizio, principio de contracción de Banach, método de la transformada de Khalouta, método de descomposición de Adomian (es)
Descargas
In this paper, we study new results regarding the existence, uniqueness and convergence of the solution of nonlinear fractional Volterra integrodifferential equations via Caputo-Fabrizio operator. The main results of this paper are based on the Banach contraction principle. Furthermore, we investigate the approximate analytical solutions of the proposed problem using a new combination method called Khalouta decomposition method. Some illustrated examples of our results are provided with some numerical simulations of the solutions.
En este artículo estudiamos nuevos resultados sobre la existencia, unicidad y convergencia de la solución de ecuaciones integro-diferenciales fraccionarias no lineales de Volterra mediante el operador Caputo-Fabrizio. Los principales resultados de este artíıculo se basan en el principio de contracción de Banach. Además, investigamos las soluciones analíticas aproximadas del problema propuesto utilizando un nuevo método de combinación llamado método de descomposición de Khalouta. Se proporcionan algunos ejemplos ilustrados de nuestros resultados con algunas simulaciones numéricas de las soluciones.
Referencias
[1] K. A. Abro, A. Atangana, and J. F. Gómez-Aguilar, A comparative analysis of plasma dilution based on fractional integro-differential equation: an application to biological science, International Journal of Analysis and Applications 43 (2023), no. 1, 1-10.
[2] S. E. Alhazmi and M. A. Abdou, A physical phenomenon for the fractional nonlinear mixed integro-differential equation using a general discontinuous kernel, fractal and fractional 7 (2023), no. 2, 1-19.
[3] S. M. Atshan and A. A. Hamoud, Approximate solutions of fourth-order fractional integro-differential equations, Acta Universitatis Apulensis 55 (2018), 49-61.
[4] E. A. Az-Zo’bi, W. A. AlZoubi, L. Akinyemi, M. S¸enol, I. W. Alsaraireh, and M. Mamat, Abundant closed-form solitons for time-fractional integrodifferential equation in fluid dynamics, Optical and Quantum Electronics 132 (2021), https://doi.org/10.1007/s11082-021-02782-6.
[5] M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications 1 (2015), no. 2, 73-85.
[6] H. Dehestani and Y. Ordokhani, An efficient approach based on legendregauss-lobatto quadrature and discrete shifted hahn polynomials for solving caputo-fabrizio fractional volterra partial integro-differential equations, Journal of Computational and Applied Mathematics 403 (2022), 113851.
[7] A. A. Hamoud and K. P. Ghadle, Existence and uniqueness results for fractional volterra-fredholm integro-differential equations, International Journal of Open Problems in Computer Science and Mathematics 11 (2018), no. 3, 16-30.
[8] A. A. Hamoud, K. P. Ghadle, and S. M. Atshan, Usage of the homotopy analysis method for solving fractional volterra-fredholm integro-differential equation of the second kind, Tamkang Journal of Mathematics 49 (2018), no. 4, 301-315.
[9] A. A. Hamoud, K. P. Ghadle, and S. M. Atshan, The approximate solutions of fractional integro-differential equations by using modified adomian decomposition method, Khayyam Journal of Mathematics 5 (2019), no. 1, 39-57.
[10] J. Hou, B. Qin, and Ch. Yang, Numerical solution of nonlinear fredholm integro-differential equations of fractional order by using hybrid functions and the collocation method, Journal of Applied Mathematics 2012 (2012), 1-11, DOI: 10.1155/2012/687030.
[11] A. Khalouta, A new exponential type kernel integral transform: Khalouta transform and its applications, Mathematica Montisnigri 57 (2023), 5-23, DOI: 10.20948/mathmontis-2023-57-1.
[12] J. Losada and J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications 1 (2015), no. 2, 87-92.
[13] S. Sabermahani, Y. Ordokhani, K. Rabiei, and M. Razzaghi, Solution of optimal control problems governed by volterra integral and fractional integro-differential equations, Journal of Vibration and Control 29 (2023), no. 15-16, 3796-3808.
[14] L. Tadoummant and R. Echarghaoui, A numerical scheme of a fractional coupled system of volterra integro-differential equations with the caputo fabrizio fractional derivative, Contemporary Mathematics 5 (2024), no. 1, 3740-3761.
[15] V. E. Tarasov, Fractional integro-differential equations for electromagnetic waves in dielectric media, Theoretical and Mathematical Physics 158 (2009), 355-359.
[16] A. M. Wazwaz, Linear and nonlinear integral equations, methods and applications, New York, 2011.
[17] F. Youbi, S. Momani, S. Hasan, and M. Al-Smadi, Effective numerical technique for nonlinear caputo-fabrizio systems of fractional volterra integrodifferential equations in hilbert space, Alexandria Engineering Journal 61 (2022), 1778-1786.
[18] Y. Zhou, Basic theory of fractional differential equations, Singapore:World Scientific, 2014.
[19] Y. Zhu, Q. Chang, and S. Wu, A new algorithm for calculating adomian polynomials, Applied Mathematics and Computation 169 (2005), 402-416.
