AN EFFECTIVE METHOD FOR SOLVING THE MULTI TIME-FRACTIONAL TELEGRAPH EQUATION OF DISTRIBUTED ORDER BASED ON THE FRACTIONAL ORDER GEGENBAUER WAVELET

被引：0
作者：
Park, C. [1 ]
Rezaei, H. [2 ]
Derakhshan, M. H. [2 ]
机构：
[1] Hanyang Univ, Res Inst Convergence Basic Sci, Dept Math, Seoul 04763, South Korea
[2] Univ Yasuj, Coll Sci, Dept Math, Yasuj 7591474831, Iran
来源：
APPLIED AND COMPUTATIONAL MATHEMATICS | 2025年 / 24卷 / 01期
关键词：
Fractional-Order; Gegenbauer Wavelet; Distributed Order; Regularized; Beta Func- tion; Telegraph Equation; NUMERICAL-METHOD; DIFFERENTIAL-EQUATIONS; DIFFUSION EQUATION; SCHEMES;
D O I：
10.30546/1683-6154.24.1.2025.16
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate an effective method for solving the multi-time fractional telegraph equation of distributed order, combining the Regularized Beta function with the fractional- order Gegenbauer wavelet. In the first stage, we define the fractional-order Gegenbauer wavelet and then approximate the solution using this wavelet. We present an exact formula that incorporates the Regularized Beta function to compute the Riemann-Liouville fractional integral of this wavelet. The wavelet, along with the exact formula, is then applied to derive numerical solutions for the multidimensional time-fractional telegraph equation of distributed order. Utilizing the midpoint rule for the distributed integral term, we transform the fractional equation of distributed order into a multi-term fractional time-differential equation. The fractional derivative is employed in the Caputo sense, allowing us to reduce the numerical solutions of the multidimensional time-fractional telegraph equations to a system of algebraic equations. We provide an in-depth analysis of the convergence and error bounds of the proposed method. The applicability and efficiency of this methodology are demonstrated through four illustrative examples. Additionally, a comparison with existing results highlights the advantages of our numerical approach.
引用
收藏
页码：16 / 37
页数：22
相关论文
共 45 条
  • [1] Abdeljawad T., Shah K., Abdo M.S., Jarad F., An analytical study of fractional delay impulsive implicit systems with Mittag-Leffler law, Appl. Comput. Math, 2, 1, pp. 31-44, (2023)
  • [2] Agarwal G., Yadav L.K., Nisar K.S., Alqarni M.M., Mahmoud E.E., A hybrid method for the analytical solution of time fractional Whitham-Broer-Kaup equations, Appl. Comput. Math, 23, 1, pp. 3-17, (2024)
  • [3] Ahmad B., Alsaedi A., Ntouyas S.K., Alotaibi F.M., A coupled Hilfer-Hadamard fractional differential system with nonlocal fractional integral boundary conditions, TWMS J. Pure Appl. Math, 15, 1, pp. 95-114, (2024)
  • [4] Ahmed H.M., Ahmed A.M., Ragusa M.A., On some non-instantaneous impulsive differential equations with fractional Brownian motion and Poisson jumps, TWMS J. Pure Appl. Math, 14, 1, pp. 125-140, (2023)
  • [5] Atanackovic T., A generalized model for the uniaxial isothermal deformation of a viscoelastic body, Acta Mech, 159, 1-4, pp. 77-86, (2002)
  • [6] Bockstal K., Existence and uniqueness of a weak solution to a non-autonomous time-fractional diffusion equation (of distributed order), Appl. Math. Lett, 109, (2020)
  • [7] Caputo M., Mean fractional order derivatives differential equations and filters, Ann. Univ. Ferrara, 41, 1, pp. 73-84, (1995)
  • [8] Camargo R.F., Chiacchio A.O., de Oliveira E.C., Differentiation to fractional orders and the fractional telegraph equation, J. Math. Phys, 49, 3, (2008)
  • [9] Celik I., Gegenbauer wavelet collocation method for the extended Fisher-Kolmogorov equation in two dimen-sions, Math. Methods Appl. Sci, 43, 8, pp. 5615-5628, (2020)
  • [10] Celik B., Akdemir A.O., Set E., Aslan S., Ostrowski-Mercer type integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators, TWMS J. Pure Appl. Math, 15, 2, pp. 269-285, (2024)
12345