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Numerical Investigation of Fractional Third-Order Differential Equation Using Quartic B-Spline Functions

Author

Listed:
  • Syeda Alishba Batool
  • Muhammad Abbas
  • Madiha Shafiq
  • Y. S. Hamed
  • Asnake Birhanu

Abstract

Fractional calculus (FC) has become more popular during the past four decades due to its extensive applications in mathematics, physics, engineering, and statistics. B-spline functions offer flexible and incredibly precise approximations because of their piecewise polynomial structure and smoothness at knots. For a class of third-order conformable boundary value problems (BVPs), we develop approximation solutions using the quartic B-spline method. The conformable fractional derivative (CFD) is utilized to formulate fractional problems. More specifically, singularities are used to modify the category of conformable Lane–Emden models. Three numerical examples are shown and examined to demonstrate the approach’s effectiveness. The numerical results are highly accurate and require less computational work, and they closely match the exact solutions.MSC2020 Classification: 39A12, 39B62, 33B10, 26A48, 26A51.

Suggested Citation

  • Syeda Alishba Batool & Muhammad Abbas & Madiha Shafiq & Y. S. Hamed & Asnake Birhanu, 2026. "Numerical Investigation of Fractional Third-Order Differential Equation Using Quartic B-Spline Functions," Advances in Mathematical Physics, Hindawi, vol. 2026, pages 1-13, March.
    • Handle: RePEc:hin:jnlamp:4100983
    DOI: 10.1155/admp/4100983
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