New results regarding the existence, uniqueness and convergence of the solution for nonlinear fractional Volterra integro-differential equations via Caputo-Fabrizio operator

• Autores: Moufida Guechi, Ali Khalouta
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 58, Nº. 1, 2024, págs. 81-98
• Idioma: varios idiomas
• Títulos paralelos:
  • 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
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • [1] K. A. Abro, A. Atangana, and J. F. Gómez-Aguilar, A comparative analysis of plasma dilution based on fractional integro-differential equation:...
  • [2] S. E. Alhazmi and M. A. Abdou, A physical phenomenon for the fractional nonlinear mixed integro-differential equation using a general...
  • [3] S. M. Atshan and A. A. Hamoud, Approximate solutions of fourth-order fractional integro-differential equations, Acta Universitatis Apulensis...
  • [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...
  • [5] M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, Progress in Fractional Differentiation and...
  • [6] H. Dehestani and Y. Ordokhani, An efficient approach based on legendregauss-lobatto quadrature and discrete shifted hahn polynomials for...
  • [7] A. A. Hamoud and K. P. Ghadle, Existence and uniqueness results for fractional volterra-fredholm integro-differential equations, International...
  • [8] A. A. Hamoud, K. P. Ghadle, and S. M. Atshan, Usage of the homotopy analysis method for solving fractional volterra-fredholm integro-differential...
  • [9] A. A. Hamoud, K. P. Ghadle, and S. M. Atshan, The approximate solutions of fractional integro-differential equations by using modified...
  • [10] J. Hou, B. Qin, and Ch. Yang, Numerical solution of nonlinear fredholm integro-differential equations of fractional order by using hybrid...
  • [11] A. Khalouta, A new exponential type kernel integral transform: Khalouta transform and its applications, Mathematica Montisnigri 57 (2023),...
  • [12] J. Losada and J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progress in Fractional Differentiation...
  • [13] S. Sabermahani, Y. Ordokhani, K. Rabiei, and M. Razzaghi, Solution of optimal control problems governed by volterra integral and fractional...
  • [14] L. Tadoummant and R. Echarghaoui, A numerical scheme of a fractional coupled system of volterra integro-differential equations with the...
  • [15] V. E. Tarasov, Fractional integro-differential equations for electromagnetic waves in dielectric media, Theoretical and Mathematical...
  • [16] A. M. Wazwaz, Linear and nonlinear integral equations, methods and applications, New York, 2011. DOI: https://doi.org/10.1007/978-3-642-21449-3
  • [17] F. Youbi, S. Momani, S. Hasan, and M. Al-Smadi, Effective numerical technique for nonlinear caputo-fabrizio systems of fractional volterra...
  • [18] Y. Zhou, Basic theory of fractional differential equations, Singapore:World Scientific, 2014. DOI: https://doi.org/10.1142/9069
  • [19] Y. Zhu, Q. Chang, and S. Wu, A new algorithm for calculating adomian polynomials, Applied Mathematics and Computation 169 (2005), 402-416....