Accès libre

An efficient algorithm for solving the conformable time-space fractional telegraph equations

À propos de cet article

Citez

[1] Abdeljawad, T. On conformable fractional calculus. J. Comp. Appl. Math. 279 (2015), 57–66.10.1016/j.cam.2014.10.016 Search in Google Scholar

[2] Banasiak, J., and Mika, J. Singular perturbed telegraph equations with applications in the random walk theory. J. Appl. Math. Stoch. Anal. 11 (1998), 9–28. Search in Google Scholar

[3] Berwal, N., Panchal, D., and Parihar, C. L. Haar waveleet method for numerical solution of telegraph equations. Ital. J. Pure Appl. Math. 30 (2013), 317–328. Search in Google Scholar

[4] Bhrawy, A., Zaky, M., and Machado, J. Numerical solution of the two-sided space and time fractional telegraph equation via chebyshev tau approximation. J. Optim. Theory Appl. (2016).10.1007/s10957-016-0863-8 Search in Google Scholar

[5] Bhrawy, A., Zaky, M., and Machado, J. Numerical solution of the two-sided spacetime fractional telegraph equation via chebyshev tau approximation. Journal of Optimization Theory and Applications 174, 1 (2017), 321–341. Search in Google Scholar

[6] Brahim, N. Numerical approach of the nonlinear reaction-advection-diffusion equation with time-space conformable fractional derivatives. AIP Conference Proceedings 2334, 060012 (2021).10.1063/5.0042459 Search in Google Scholar

[7] Brahim, N., and Benyattou, B. Newmark method applied to the elasto-dynamic problem with slip-rate dependent friction. Journal of Concrete & Applicable Mathematics 7, 1 (2009), 70–81. Search in Google Scholar

[8] Cattani, C., Srivastava, H. M., and Yang, X. J. Fractional Dynamics. de Gruyter, Berlin, 2016.10.1515/9783110472097 Search in Google Scholar

[9] Chen, J., Liu, F., and Anh, V. Analytical solution for the time-fractional telegraph equation by the method of separating variables. Journal of Mathematical Analysis and Applications 338, 2 (2008), 1364–1377. Search in Google Scholar

[10] ş. Yüzbaşi. Numerical solutions of hyperbolic telegraph equation by using the bessel functions of first kind and residual correction. Applied Mathematics and Computation 287 (2016), 83–93.10.1016/j.amc.2016.04.036 Search in Google Scholar

[11] ş. Yüzbaşi. A shifted legendre method for solving a population model and delay linear volterra integrodifferential equations. International Journal of Biomathematics 10, 7 (2017), p.1750091.10.1142/S1793524517500917 Search in Google Scholar

[12] Dehghan, M., and Ghesmati, A. Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (drbie) method. Eng. Anal. Bound. Elements 34 (2010), 51–59. Search in Google Scholar

[13] Dehghan, M., and Shokri, A. A numerical method for solving the hyperbolic telegraph equation. Numer. Methods Partial Differ. Equ. 24 (2008), 1080–1093.10.1002/num.20306 Search in Google Scholar

[14] Heaviside, O. Electromagnetic theory. Chelsea Publishing Company, New York, Vol-2, 1899. Search in Google Scholar

[15] Heydari, M., Hooshmandasl, M., and Mohammadi, F. Two-dimensional legendre wavelets for solving time-fractional telegraph equation. Advances in Applied Mathematics and Mechanics 6, 2 (2014), 247–260. Search in Google Scholar

[16] Javidi, M. Chebyshev spectral collocation method for computing numerical solution of telegraph equation. Comput. Methods Differ. Equ. 1 (2013), 16–29. Search in Google Scholar

[17] Jordan, P., and Puri, A. Digital signal propagation in dispersive media. J. Appl. Phys. 85 (1999), 1273–1283. Search in Google Scholar

[18] Khalil, R., AlHorani, M., Yousef, A., and Sababheh, M. A new definition of fractional derivative. J. Comp. Appl. Math. 264 (2014), 65–70. Search in Google Scholar

[19] Kumar, D., Singh, J., and Kumar, S. Analytic and approximate solutions of space-time fractional telegraph equations via laplace transform. Walailak Journal of Science and Technology (WJST) 11, 8 (2013), 711–728. Search in Google Scholar

[20] Kumar, S. A new analytical modelling for fractional telegraph equation via laplace transform. Applied Mathematical Modelling 38, 11 (2014), 3154–3163. Search in Google Scholar

[21] Mason, J., and Handscomb, D. Chebyshev Polynomials. Chapman and Hall, CRC, New York, NY, Boca Raton, 2003.10.1201/9781420036114 Search in Google Scholar

[22] Metaxas, A., and Meredith, R. Industrial microwave heating. Peter Peregrinus, London, UK, 1993. Search in Google Scholar

[23] Mittal, R., and Bhatia, R. Numerical solution of second order one dimensional hyperbolic telegraph equation by cubic b-spline collocation method. Appl. Math. Comput. 220 (2013), 496–506. Search in Google Scholar

[24] Mohyud-Din, S. T., Yldrm, A., and Kaplan, Y. Homotopy perturbation method for one-dimensional hyperbolic equation with integral conditions. J. Phys. Sci. 65 (2010), 1077–1080. Search in Google Scholar

[25] Mollahasani, N., Moghadam, M. M., and Afrooz, K. A new treatment based on hybrid functions to the solution of telegraph equations of fractional order. Applied Mathematical Modelling 40, 4 (2016), 2804–2814. Search in Google Scholar

[26] Momani, S. Analytic and approximate solutions of the space- and time-fractional telegraph equations. Applied Mathematics and Computation 170, 2 (2005), 1126–1134. Search in Google Scholar

[27] Muthukumar, P., and Priya, B. Numerical solution of fractional delay differential equation by shifted jacobi polynomials. International Journal of Computer Mathematics 94, 3 (2017), 471–492. Search in Google Scholar

[28] Nazir, T., Abbas, M., and Yaseen, M. Numerical solution of second-order hyperbolic telegraph equation via new cubic trigonometric bsplines approach. Cogent Mathematics 4 (2017), 1382061.10.1080/23311835.2017.1382061 Search in Google Scholar

[29] Newmark, N. M. A method of computation for structural dynamics. ASCE Journal of Engineering Mechanics Division 85 (1959), 67–94. Search in Google Scholar

[30] Pekmen, B., and Tezer-Sezgin, M. Differential quadrature solution of hyperbolic telegraph equation. J. Appl. Math. (2012), 18.10.1155/2012/924765 Search in Google Scholar

[31] Podlubny, I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Academic press, 1998. Search in Google Scholar

[32] Prakash, A. Analytical method for space-fractional telegraph equation by homotopy perturbation transform method. Nonlinear Engineering 5, 2 (2016), 123128.10.1515/nleng-2016-0008 Search in Google Scholar

[33] Razmjooy, N., and Ramezani, M. Analytical solution for optimal control by the second kind chebyshev polynomials expansion. Iranian Journal of Science and Technology, Transactions A: Science 41, 4 (2017), 1017–1026. Search in Google Scholar

[34] Saadatmandi, A., and Dehghan, M. Numerical solution of hyperbolic telegraph equation using the chebyshev tau method. Numer. Methods Partial Differ. Equ. 26 (2010), 239–252.10.1002/num.20442 Search in Google Scholar

[35] Saadatmandi, A., and Mohabbati, M. Numerical solution of fractional telegraph equation via the tau method. Math. Rep. 17 (2015), 155–166. Search in Google Scholar

[36] Samko, S., Kilbas, A., and Marichev, O. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Langhorne, 1993. Search in Google Scholar

[37] Sevimlican, A. An approximation to solution of space and time fractional telegraph equations by he’s variational iteration method. Mathematical Problems in Engineering 2010 (2010).10.1155/2010/290631 Search in Google Scholar

[38] Sharifi, S., and Rashidinia, J. Numerical solution of hyperbolic telegraph equation by cubic b-spline collocation method. Applied Mathematics and Computation 281 (2016), 28–38. Search in Google Scholar

[39] Shivanian, E. Spectral meshless radial point interpolation (smrpi) method to two-dimensional fractional telegraph equation. Math. Methods Appl. Sci. (2015).10.1002/mma.3604 Search in Google Scholar

[40] Singh, H., Pandey, K. R., and Baleanu, D. Stable numerical approach for fractional delay differential equations. Few-Body Systems 58, 6 (2017), 156.10.1007/s00601-017-1319-x Search in Google Scholar

[41] Suleman, M., Elzaki, T., Rahman, J., and Wu, Q. A novel technique to solve space and time fractional telegraph equation. Journal of Computational and Theoretical Nanoscience 13, 3 (2016), 1536–1545. Search in Google Scholar

[42] Sweilam, N., Nagy, A., and El-Sayed, A. Solving time-fractional order telegraph equation via sinclegendre collocation method. Mediterranean Journal of Mathematics 13, 6 (2016), 5119–5133. Search in Google Scholar

[43] Weston, V., and He, S.Wave splitting of the telegraph equation in ℝ and its application to inverse scattering. Inverse Problems 9 (1993), 789–812. Search in Google Scholar

[44] Yildirim, A. He’s homotopy perturbation method for solving the space- and time-fractional telegraph equations. International Journal of Computer Mathematics 87, 13 (2010), 2998–3006. Search in Google Scholar

[45] Yousefi, S. A. Legendre multiwavelet galerkin method for solving the hyperbolic telegraph equation. Numer. Methods Partial Differ. Equ. 26 (2010), 535–543. Search in Google Scholar