Spectral Fractional-Order Method for Solving Nonlinear Weakly Singular Volterra Integral Equations

被引：0
|
作者：
Razaghzadeh, N. [1 ]
Moghad, Mohseni M. [2 ,3 ]
Saeedi, H. [2 ,3 ]
机构：
[1] Grad Univ Adv Technol, Fac Sci & New Technol, Dept Math, Kerman, Iran
[2] Shahid Bahonar Univ Kerman, Mahani Math Res Ctr, Kerman, Iran
[3] Shahid Bahonar Univ Kerman, Fac Math, Dept Appl Math, Kerman, Iran
来源：
MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES | 2020年 / 14卷 / 03期
关键词：
Operational matrix of fractional integration; weakly singular Volterra equations; 1ST KIND; INVERSION; CALCULUS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we present a spectral method based on fractional-order Jacobi functions and their new constructed operational matrix of fractional integration for solving nonlinear weakly singular Volterra integral equations which include Abel equations. A proposed error analysis investigates the convergence of mentioned method. Some numerical examples are presented to confirm the efficiency and accuracy of the method.
引用
收藏
页码：543 / 564
页数：22
相关论文
共 50 条
  • [31] A product integration method for nonlinear second kind Volterra integral equations with a weakly singular kernel (with application to fractional differential equations)
    Katani, R.
    Mckee, S.
    APPLIED MATHEMATICS LETTERS, 2025, 163
  • [32] Convergence analysis of Jacobi spectral tau-collocation method in solving a system of weakly singular Volterra integral equations
    Mostafazadeh, Mahdi
    Shahmorad, Sedaghat
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 223 : 322 - 337
  • [33] Fractional-order Euler functions for solving fractional integro-differential equations with weakly singular kernel
    Wang, Yanxin
    Zhu, Li
    Wang, Zhi
    ADVANCES IN DIFFERENCE EQUATIONS, 2018,
  • [34] Fractional-order Euler functions for solving fractional integro-differential equations with weakly singular kernel
    Yanxin Wang
    Li Zhu
    Zhi Wang
    Advances in Difference Equations, 2018
  • [35] SOLVING NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS OF SECOND KIND BY THE ADOMIAN METHOD
    Seny, Ouedraogo
    Loufouilou, Justin Mouyedo
    Joseph, Bonazebi Yindoula
    Pare, Youssouf
    ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS, 2022, 29 (01): : 97 - 110
  • [36] The Jacobi Collocation Method for a Class of Nonlinear Volterra Integral Equations with Weakly Singular Kernel
    Allaei, Sonia Seyed
    Diogo, Teresa
    Rebelo, Magda
    JOURNAL OF SCIENTIFIC COMPUTING, 2016, 69 (02) : 673 - 695
  • [37] Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method
    Ali, Mohamed R.
    Mousa, Mohamed M.
    Ma, Wen-Xiu
    ADVANCES IN MATHEMATICAL PHYSICS, 2019, 2019
  • [38] The Jacobi Collocation Method for a Class of Nonlinear Volterra Integral Equations with Weakly Singular Kernel
    Sonia Seyed Allaei
    Teresa Diogo
    Magda Rebelo
    Journal of Scientific Computing, 2016, 69 : 673 - 695
  • [39] Solving a System of Fractional-Order Volterra-Fredholm Integro-Differential Equations with Weakly Singular Kernels via the Second Chebyshev Wavelets Method
    Bargamadi, Esmail
    Torkzadeh, Leila
    Nouri, Kazem
    Jajarmi, Amin
    FRACTAL AND FRACTIONAL, 2021, 5 (03)
  • [40] Spectral methods for weakly singular Volterra integral equations with smooth solutions
    Chen, Yanping
    Tang, Tao
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 233 (04) : 938 - 950
12345