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Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.In this sequel, we employ an approach that combines the modified version of the Lagrange polynomial approximation technique with the biconjugate gradient stabilized method (BiCGSTAB) to analyze numerical solutions of fractional Volterra integral equations (FVIEs).
Imtiyaz Ahmad Bhat +3 more
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Fractal and Fractional, 2023 The nonlinear Volterra–Fredholm integral Equation (NVFIE) with a singular kernel is discussed such that the kernel of position can take the Hilbert kernel form, Carleman function, logarithmic form, or Cauchy kernel. Using the quadrature method, the NVFIE
Sahar M. Abusalim +3 more
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Computers & Mathematics with Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Esmail Babolian +3 more
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On the approximate solution of nonlinear Volterra-Fredholm integral equations on a complex domain by Dzyadyk’s method [PDF]
Ukrainian Mathematical Journal, 1997 \textit{V. K. Dzyadyk} [Colloq. Math. Soc. János Bolyai. 35, 441-448 (1983; Zbl 0574.34009)] proposed an iterative approximation method for the numerical solution of the Cauchy problem for ordinary differential equations. Later this method was developed and applied for the numerical solution of different types of differential and integral equations. In
Rizk, M. M., Zaher, S. L.
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Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.High‐order fractional fuzzy differential equations show great potential in modeling complex systems with memory effects and uncertainty. Existing qualitative theories seldom involve both Caputo‐type strongly generalized Hukuhara differentiability and coupled integral operators on infinite intervals. This paper presents a systematic investigation of the
Yanli Xi +2 more
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Numerical treatments for solving nonlinear mixed integral equation
Alexandria Engineering Journal, 2016 We consider a mixed type of nonlinear integral equation (MNLIE) of the second kind in the space C[0,T]×L2(Ω ...
M.A. Abdou, M. Basseem
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.In the present article, an emerging subdivision‐based technique is developed for the numerical solution of linear Volterra partial integrodifferential equations (LVPIDEs) of order four with a weakly singular kernel. To approximate the spatial derivatives, the basis function of the subdivision scheme is used, whereas the time discretization is done with
Zainab Iqbal +5 more
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.This paper studies a nonlinear hybrid Ψ‐Liouville–Caputo–Katugampola fractional integro‐differential equation. The proposed problem contains functional, Volterra integral, and delay terms. First, we derive the corresponding fractional integral equation. The problem is studied in the Banach algebra X=CJ,ℝ endowed with the supremum norm.
Alireza Hatami +2 more
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Numerical method for the mixed Volterra-Fredholm integral equations using hybrid Legendre functions [PDF]
, 2015 summary:A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise ...
Lima, P., Ordokhani, Y., Nemati, S.
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.This paper investigates a class of nonlinear implicit neutral integrodifferential equations involving Hilfer–Katugampola fractional operators, which provide an effective framework for describing dynamical systems with memory and hereditary properties. By converting the considered problem into an equivalent fractional integral equation, we show that the
Manal Elzain Mohamed Abdalla +3 more
wiley +1 more source