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<p>Numerous fixed-point theorems (FPTs) are crucial for scientific research in the domains of engineering and science. The main goal of this article is to examine the Ulam-Hyers stability for fractional integro-differential equations with Atangana-Baleanu-Caputo (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{A}\mathcal{B}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">A</mi> <mi mathvariant="script">B</mi> </mrow> </math></EquationSource> </InlineEquation>-Caputo) fractional derivative in a Banach space. Moreover, Banach Contraction Mapping Principle (BCMP) and Krasnoselskii fixed-point theorems (KFPT) are utilized to prove the uniqueness and existence theorems. In the end, an example is discussed to validate the analytical result, and a two-step Lagrange polynomial interpolation method is utilized to solve some numerical examples.</p>

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An Efficient Numerical Methods of Ulam Stability and Atangana-Baleanu-Caputo Fractional Equations with Integral Boundary Conditions

  • 期刊论文

  • 发表日期：

    2025年11月14日

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  • K. Venkatachalam,
  • M. Sathish Kumar,
  • M. Asick Ali,
  • V. Pushpalatha

摘要

Numerous fixed-point theorems (FPTs) are crucial for scientific research in the domains of engineering and science. The main goal of this article is to examine the Ulam-Hyers stability for fractional integro-differential equations with Atangana-Baleanu-Caputo ( \(\mathcal{A}\mathcal{B}\) A B -Caputo) fractional derivative in a Banach space. Moreover, Banach Contraction Mapping Principle (BCMP) and Krasnoselskii fixed-point theorems (KFPT) are utilized to prove the uniqueness and existence theorems. In the end, an example is discussed to validate the analytical result, and a two-step Lagrange polynomial interpolation method is utilized to solve some numerical examples.