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August 15, 2025Scientific ReportsOpen Access

A numerical approach to fractional Volterra–Fredholm integro-differential problems using shifted Chebyshev spectral collocation

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Authors

MHMaha M. HamoodHodeidah UniversityASAbdulrahman A. SharifDr. Babasaheb Ambedkar Marathwada UniversityKGKirtiwant P. GhadleDr. Babasaheb Ambedkar Marathwada University

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Overview

This approach demonstrates high-order accuracy in initial value problems using a shifted Chebyshev method, suggesting improved computational efficiency.

Key Points

  • The method achieves high-order accuracy in solving fractional volterra–fredholm integro-differential equations, enhancing numerical precision.
  • Using benchmark examples, the framework shows significant stability and efficiency in computational tasks related to IVPs.
  • A spectral collocation method is employed, ensuring rapid convergence via the newton–raphson iteration for effective problem-solving.
  • The findings highlight the applicability of this numerical framework in various fields of applied mathematics and engineering.

Cite This Study

Hamood et al. (2025) studied this question.

synapsesocial.com/papers/68a3654c0a429f797332b024https://doi.org/10.1038/s41598-025-13732-7
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Also Consider

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  1. 1A Direct Polynomial Solution of Nonlinear Volterra-Fredholm Integro-Differential Equations via the Shifted Chebyshev Collocation Method2026
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  3. 3A highly accurate Hermite polynomial-based least-squares approach for solving fractional Volterra-Fredholm integro-differential equations2026 · 1 citations
  4. 4Utilizing Cubic B-Spline Collocation Technique for Solving Linear and Nonlinear Fractional Integro-Differential Equations of Volterra and Fredholm Types2024 · 2 citations
  5. 5Theoretical and Numerical Studies of Fractional Volterra-Fredholm Integro-Differential Equations in Banach Space2024 · 3 citations