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Ilie, Mousa, Khoshkenar, Ali, Torabi Giklou, Asadollah. (1403). Solving a class of Volterra integral equations with M-derivative. سامانه مدیریت نشریات علمی, 13(1), 282-293. doi: 10.22034/cmde.2024.58936.2498
Mousa Ilie; Ali Khoshkenar; Asadollah Torabi Giklou. "Solving a class of Volterra integral equations with M-derivative". سامانه مدیریت نشریات علمی, 13, 1, 1403, 282-293. doi: 10.22034/cmde.2024.58936.2498
Ilie, Mousa, Khoshkenar, Ali, Torabi Giklou, Asadollah. (1403). 'Solving a class of Volterra integral equations with M-derivative', سامانه مدیریت نشریات علمی, 13(1), pp. 282-293. doi: 10.22034/cmde.2024.58936.2498
Ilie, Mousa, Khoshkenar, Ali, Torabi Giklou, Asadollah. Solving a class of Volterra integral equations with M-derivative. سامانه مدیریت نشریات علمی, 1403; 13(1): 282-293. doi: 10.22034/cmde.2024.58936.2498

Solving a class of Volterra integral equations with M-derivative

Computational Methods for Differential Equations
مقاله 21، دوره 13، شماره 1، فروردین 2025، صفحه 282-293    اصل مقاله (642.34 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.58936.2498
نویسندگان
Mousa Ilie* 1؛ Ali Khoshkenar1؛ Asadollah Torabi Giklou2
1Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
2Department of Basic Sciences, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran.
چکیده
In this current article, the well-known Neumann method for solving the time M-fractional Volterra integral equations of the second kind is developed. In the several theorems, existence and uniqueness of the solution and convergence of the proposed approach are also studied. The Neumann method for this class of the time M-fractional Volterra integral equations has been called the M-fractional Neumann method (MFNM). The results obtained demonstrate the efficiency of the proposed method for the time M-fractional Volterra integral equations. Several illustrative numerical examples have presented the ability and adequacy of the MFNM for a class of fractional integral equations.
کلیدواژه‌ها
Local M-fractional integral؛ M-fractional Volterra integral equations؛ M-fractional Neumann method؛ Existence and uniqueness of solution؛ Theorem of convergence
مراجع
  • [1] E. M. Abdelghany, W. M. Abd-Elhameed, G. M. Moatimid, Y. H. Youssri, and A. G. Atta, A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials, Symmetry, 15(594) (2023).
  • [2] W. A. Ahmood and A. Kilicman, Solutions of linear multi-dimensional fractional order Volterra integral equations, Journal of Theoretical and Applied Information Technology, 89 (2016), 381-388.
  • [3] R. Agarwal, S. Jain, and R. P. Agarwal, Solution of fractional Volterra integral equation and non-homogeneous time fractional heat equation using integral transform of pathway type, Progress in Fractional Differentiation and Applications, 1 (2015), 145-155.
  • [4] A. Asanov, R. Almeida, and A. B. Malinowska, Fractional differential equations and Volterra–Stieltjes integral equations of the second kind, Computational and Applied Mathematics, 38(160) (2019).
  • [5] A. Atangana and N. Bildik, Existence and numerical solution of the Volterra fractional integral equations of the second kind, Mathematical Problems in Engineering, (2013).
  • [6] A. G. Atta and Y. H. Youssri, Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel, Computational & amp; Applied Mathematics, 41(381) (2022).
  • [7] E. Bonyah, M. Yavuz, D. Baleanu, and S. Kumar, A robust study on the listeriosis disease by adopting fractalfractional operators, Alexandria Engineering Journal, 61(3) (2022), 2016-202.
  • [8] E. C. De Oliveira and J. A. Tenreiro Machado, A review of definitions for fractional derivatives and integral, Mathematical Problems in Engineering, (2014), 238459.
  • [9] L. M. Delves and J. L. Mohamed, Computational methods for integral equations, Cambridge University Press, 1985.
  • [10] S. Duran, H. Durur, M. Yavuz, and A. Yokus, Discussion of numerical and analytical techniques for the emerging fractional order murnaghan model in materials science, Optical and Quantum Electronic, 55(571) (2023).
  • [11] S. Esmaeili, M. Shamsi, and M. Dehghan, Numerical solution of fractional differential equations via a Volterra integral equation approach, Open Physics, 11(10) (2013), 1470-1481.
  • [12] R. Goreno, A. A. Kilbas, F. Mainardi, and S. V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications, Springer, Berlin, 2014.
  • [13] R. M. Hafez and Y. H. Youssri, Shifted Jacobi collocation scheme for multidimensional time-fractional order telegraph equation, Iranian Journal of Numerical Analysis and Optimization, 10(1-17) (2020), 195-225.
  • [14] M. Ilie, J. Biazar, and Z. Ayati, Neumann method for solving conformable fractional Volterra integral equations, Computational Methods for Differential Equations, 8(1) (2020), 54-68.
  • [15] M. Ilie and A. Khoshkenar, Resonant solitons solutions to the time M-fractional Schr¨odinger equation, Iranian Journal of Optimization, 13(3) (2022), 197-210.
  • [16] M. Ilie and A. Khoshkenar, A novel study on nonlinear fractional differential equations: general solution, Iranian Journal of Optimization, 14(4) (2023).
  • [17] A. Khoshkenar, M. Ilie, K. Hosseini, D. Baleanu, S. Salahshour, and J. R. Lee, Further studies on ordinary differential equations involving the M-fractional derivative, AIMS MATHEMATICS, 7(6) (2023), 10977-10993.
  • [18] M. Mohammad, and A. Trounev, Fractional nonlinear Volterra–Fredholm integral equations involving AtanganaBaleanu fractional derivative: framelet applications, Advances in Difference Equations, 618 (2020).
  • [19] M. Moustafa, Y. H. Youssri, and A. G. Atta, quot;Explicit Chebyshev Petrov-Galerkin scheme for timefractional fourth-order uniform Euler–Bernoulli pinned–pinned beam equation, Nonlinear Engineering, 12(1) (2023), 20220308.
  • [20] B. A. Ozturk, Examination of Sturm-Liouville problem with proportional derivative in control theory, Mathematical Modelling and Numerical Simulation with Applications, 3(4) (2023), 335-35.
  • [21] G. F. Simmons, Differential Equations whit Applications and Historical Notes, McGraw-Hill, Inc. New York, 1974.
  • [22] F. Smithies, Integral equations, Cambridge University Press, 1958.
  • [23] M. Tariq, S. K. Sahoo, H. Ahmad, A. A. Shaikh, B. Kodamasingh, and D. Khan, Some integral inequalities via new family of preinvex functions, Mathematical Modelling and Numerical Simulation With Applications, 2(2) (2022), 117-126.
  • [24] J. Vanterler da C. Sousa, and E. Capelas de Oliveira, M-fractional derivative with classical properties, (2017), arXiv:1704.08187.
  • [25] J. Vanterler da C. Sousa, and E. Capelas de Oliveira, A New Truncated M-Fractional Derivative Type Unifying Some Fractional Derivative Types with Classical Properties, International Journal of Analysis and Applications, 16(1) (2018), 83-96.
  • [26] A. M. Wazwaz, Linear and nonlinear integral equations methods and applications, Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg, 2011.
  • [27] Y. H. Youssri and W. M. Abd-Elhameed, Numerical spectral LEGENDRE-GALERKIN algorithm for solving time fractional Telegraph equation, Romanian Journal of Physics, 63(107) (2018).
  • [28] Y. H. Youssri and A. G. Atta, Petrov-Galerkin Lucas Polynomials Procedure for the Time-Fractional Diffusion Equation, Contemporary Mathematics, (2023).
  • [29] L. Zada, R. Nawaz, K. S. Nisar, M. Tahir, M. Yavuz, M. K. A. Kaabar, and F. Mart´ınez, New approximateanalytical solutions to partial differential equations via auxiliary function method, Partial Differential Equations in Applied Mathematics, 4(100045) (2021).
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