Ir al contenido

Documat

Advancing Mathematical Physics: Insights into Solving Nonlinear Time-Fractional Equations

  • Ming Li [2] ; Wei Zhang [2] ; Raghda A. M. Att [3] ; Suleman H. Alfalqi [1] ; Jameel F. Alzaidi [1] ; Mostafa M. A. Khater [4]
    1. [1] King Khalid University

      King Khalid University

      Arabia Saudí

    2. [2] Shandong Qihong Engineering Construction Co
    3. [3] Xuzhou Medical University
    4. [4] Xuzhou Medical University & Obour High Institute for Engineering and Technolog
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
  • Idioma: inglés
  • Enlaces
  • Resumen

    • This study is centered on addressing the complexities of the nonlinear time-fractional Harry Dym equation through a combined application of analytical and numerical methodologies. The principal objective is to establish a comprehensive framework for solving this intricate fractional partial differential equation. The introduction of the Khater II method as an analytical technique presents a novel approach specifically designed to handle such equations. In tandem, the utilization of numerical schemescubic-B-spline, quantic-B-spline, and septic-B-spline methods-further refines the accuracy and efficiency of the solutions. The outcomes underscore the efficacy of these proposed methods in effectively resolving the challenges posed by the Harry Dym equation. Emphasis is placed on the dual facets of analytical insights and numerical precision. The significance of this study lies in its contribution to advancing comprehension of nonlinear time-fractional equations while offering practical tools for their resolution. The conclusions drawn from this research provide valuable insights into the practical applicability of the Khater II method and B-spline schemes in navigating complex mathematical models. The novelty of this work lies in the amalgamation of an innovative analytical approach with established numerical techniques, signifying a noteworthy contribution to this field of study.

  • Referencias bibliográficas
    • 1. Rawashdeh, M.: A new approach to solve the fractional harry dym equation using the frdtm. Int. J. Pure Appl. Math 95(4), 553–566 (2014)
    • 2. Khater, M.M.A.: Physics of crystal lattices and plasma; analytical and numerical simulations of the Gilson–Pickering equation. Results...
    • 3. Khater, M.M.A.: Hybrid accurate simulations for constructing some novel analytical and numerical solutions of three-order GNLS equation....
    • 4. Khater, M.M.: Waves in motion: unraveling nonlinear behavior through the Gilson–Pickering equation. Eur. Phys. J. Plus 138(12), 1138 (2023)
    • 5. Khater, M.M.: Advanced computational techniques for solving the modified kdv–kp equation and modeling nonlinear waves. Opt. Quant. Electron....
    • 6. Khater, M.M.: Novel constructed dark, bright and rogue waves of three models of the well-known nonlinear Schrödinger equation. Int. J....
    • 7. Khater, M.M.: Exploring the rich solution landscape of the generalized Kawahara equation: insights from analytical techniques. Eur. Phys....
    • 8. Khater, M.M.: Wave propagation and evolution in a (1+1)-dimensional spatial-temporal domain: a comprehensive study. Mod. Phys. Lett....
    • 9. Huang, Q., Zhdanov, R.: Symmetries and exact solutions of the time fractional Harry–Dym equation with Riemann–Liouville derivative. Phys....
    • 10. Khater, M.M.A.: Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation. Heliyon 9, e13511 (2023)
    • 11. Khater, M.M.A.: Multi-vector with nonlocal and non-singular kernel ultrashort optical solitons pulses waves in birefringent fibers. Chaos...
    • 12. Khater, M.M.A.: Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation. Heliyon 9, e13511 (2023)
    • 13. Khater, M.M.: Wave propagation analysis in the modified nonlinear time fractional Harry Dym equation: insights from Khater ii method and...
    • 14. Khater, M.M.: Modeling wave propagation with gravity and surface tension: soliton solutions for the generalized hietarinta-type equation....
    • 15. Yoku¸s, A., Gülbahar, S.: Numerical solutions with linearization techniques of the fractional Harry Dym equation. Appl. Math. Nonlinear...
    • 16. Khater, M.M.A.: Multi-vector with nonlocal and non-singular kernel ultrashort optical solitons pulses waves in birefringent fibers. Chaos...
    • 17. Khater, M.M.A.: In solid physics equations, accurate and novel soliton wave structures for heating a single crystal of sodium fluoride....
    • 18. Khater, M.M.A.: Prorogation of waves in shallow water through unidirectional Dullin–Gottwald–Holm model; computational simulations. Int....
    • 19. Khater,M.M.A.: Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect. Int. J....
    • 20. Kumar, D., Singh, J., Kılıçman, A., et al.: An efficient approach for fractional Harry Dym equation by using Sumudu transform. In: Abstract...
    • 21. Khater, M.M.A.: In surface tension; gravity-capillary, magneto-acoustic, and shallow water waves’ propagation. Eur. Phys. J. Plus 138(4),...
    • 22. Khater, M.M.A.: A hybrid analytical and numerical analysis of ultra-short pulse phase shifts. Chaos Solitons Fractals 169, 113232 (2023)
    • 23. Khater, M.M.A.: Long waves with a small amplitude on the surface of the water behave dynamically in nonlinear lattices on a non-dimensional...
    • 24. Khater, M.M.A.: Abundant and accurate computational wave structures of the nonlinear fractional biological population model. Int. J. Mod....
    • 25. Khater, M.M.A.: Advancements in computational techniques for precise solitary wave solutions in the (1+1)-dimensional Mikhailov–Novikov–Wang...
    • 26. Khater, M.M.A.: Numerous accurate and stable solitary wave solutions to the generalized modified equal-width equation. Int. J. Theor....
    • 27. Khater, M.M.A.: Horizontal stratification of fluids and the behavior of long waves. Eur. Phys. J. Plus 138(8), 715 (2023)
    • 28. Khater, M.M.A.: Characterizing shallow water waves in channels with variable width and depth; computational and numerical simulations....
    • 29. Khater, M.M.A.: Soliton propagation under diffusive and nonlinear effects in physical systems; (1+1)- dimensional MNW integrable equation....
    • 30. Khater, M.M.A.: Computational simulations of propagation of a tsunami wave across the ocean. Chaos Solitons Fractals 174, 113806 (2023)
    • 31. Khater, M.M.A.: Physical and dynamic characteristics of high-amplitude ultrasonic wave propagation in nonlinear and dissipative media....
    • 32. Khater, M.M.A.: Analyzing pulse behavior in optical fiber: Novel solitary wave solutions of the perturbed Chen–Lee–Liu equation. Mod....
    • 33. Kumar, S., Tripathi, M.P., Singh, O.P.: A fractional model of Harry Dym equation and its approximate solution. Ain Shams Eng. J. 4(1),...
    • 34. Al-Khaled, K., Alquran, M.: An approximate solution for a fractional model of generalized Harry Dym equation. Math. Sci. 8, 125–130 (2014)
    • 35. Costa, F.S., Soares, J.C., Plata, A.R., de Oliveira, E.C.: On the fractional Harry Dym equation. Comput. Appl. Math. 37(3), 2862–2876...
    • 36. Iyiola, O.S., Gaba, Y.U.: An analytical approach to time-fractional Harry Dym equation. Appl. Math. Inform. Sci. 10, 409–412 (2016)
    • 37. Rawashdeh, M.S.: The fractional natural decomposition method: theories and applications. Math. Methods Appl. Sci. 40(7), 2362–2376 (2017)
    • 38. Shunmugarajan, B.: An efficient approach for fractional Harry Dym equation by using homotopy analysis method. Int. J. Eng. Res. Technol....
    • 39. Kumar, D., Singh, J.: New reliable algorithm for fractional Harry Dym equation. In: Proceedings of the Second International Conference...
    • 40. Liao, S.: Comparison between the homotopy analysis method and homotopy perturbation method. Appl. Math. Comput. 169(2), 1186–1194 (2005)
    • 41. Sun, J.: Analytical approximate solutions of (n+1)-dimensional fractal Harry Dym equations. Fractals 26(06), 1850094 (2018)
    • 42. Yue, C., Liu, G., Li, K., Dong, H.: Similarity solutions to nonlinear diffusion/Harry Dym fractional equations. Adv. Math. Phys. 2021,...
    • 43. Assabaai, M.A., Mukherij, O.F.: Exact solutions of the Harry Dym equation using lie group method. Univ. Aden J. Natl. Appl. Sci. 24(2),...
    • 44. Wang, L.-Z., Wang, D.-J., Shen, S.-F., Huang, Q.: Lie point symmetry analysis of the Harry-Dym type equation with Riemann–Liouville fractional...
    • 45. Rao, T.R.: Numerical simulation of Harry Dym equation. In: AIP Conference Proceedings, Vol. 2112. AIP Publishing LLC, p. 020175 (2019)
    • 46. Soltania, D., Khorshidib, M.A.: Application of homotopy perturbation and reconstruction of variational iteration methods for harry dym...
    • 47. Nadeem, M., Li, Z., Alsayyad, Y., et al.: Analytical approach for the approximate solution of harry dym equation with caputo fractional...
    • 48. Alshammari, S., Iqbal, N., Yar, M.: Analytical investigation of nonlinear fractional Harry Dym and Rosenau–Hyman equation via a novel...
    • 49. Assabaai, M.: Numerical solution of the Harry Dym equation using Chebyshev spectral method via lie group method. In: Journal of Physics:...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno