Fully discrete RBF collocation method for linear and nonlinear one- and two-dimensional third-kind caputo-hadamard fractional delay integro-differential equations with nonlinear vanishing delays

Aourir E., Laeli Dastjerdi H., Heydari M., Shah K., Abdeljawad T.

Communications in Nonlinear Science and Numerical Simulation, cilt.161, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 161
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.cnsns.2026.110134
  • Dergi Adı: Communications in Nonlinear Science and Numerical Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Compendex, INSPEC, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Technology Collection (ProQuest)
  • Anahtar Kelimeler: Caputo–Hadamard fractional derivatives, Error analysis and convergence, Gauss–Jacobi and Gauss–Legendre quadrature, Hadamard fractional integral operators, Mesh-free collocation method, Nonlinear fractional integro–differential equations, Nonlinear vanishing delays, Radial basis functions (RBFs), Third-kind fractional delay–integro–differential equations, Two-dimensional models
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

The main aim of this study is to develop a fully discrete mesh-free radial basis function (RBF) collocation method for linear and nonlinear third-kind Caputo–Hadamard fractional delay integro–differential equations with nonlinear vanishing delays, together with their two-dimensional form. By recasting the models as equivalent Volterra–Hadamard integral equations, we establish existence and uniqueness of continuous solutions via fixed-point arguments under boundedness and contractivity assumptions. We then develop a fully discrete mesh-free RBF collocation method using Gaussian (GA) and inverse multiquadric (IMQ) trial spaces centered at shifted Chebyshev–Lobatto nodes. In the two-dimensional case, for each fixed value of x , the same RBF approximation is used with respect to the variable t . The Caputo–Hadamard term is discretized using a Gauss–Jacobi rule based on the Hadamard fractional integral representation, while the Volterra-type integral terms, including those with delay-dependent upper limits, are approximated by Gauss–Legendre quadrature. This yields dense linear systems in the linear case and nonlinear algebraic systems solved in residual form by damped Newton iterations. Convergence is proved by using operator arguments, stability of the discrete operators, and native-space approximation estimates for RBF interpolation, leading to sup-norm error bounds in terms of the fill distance and the quadrature accuracy. Numerical experiments in one and two dimensions are in agreement with the theoretical results and illustrate the accuracy of the proposed method as well as the usual accuracy–conditioning behaviour of global RBF collocation methods.