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<p>The aim of this paper is to discuss a class of semilinear fractional integro-differential equations in fractional power spaces. By using fractional calculus theory, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-resolvent operators, the Banach fixed point theorem and a generalized Gronwall inequality, we first study the existence and uniqueness of solutions for Cauchy problems. Meanwhile, the continuous dependence and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\epsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation>-continuous dependence of solutions on the initial condition are discussed. In addition, we introduce a new concept of h-Mittag-Leffler-Ulam’s type stability, and obtain the results of this type stability for the considered equations on a compact interval. Eventually, an example illustrates our results.</p>

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Continuous dependence and h-Mittag-Leffler-Ulam’s type stability for semilinear fractional integro-differential equations in fractional power spaces

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Jianbo Zhu

摘要

The aim of this paper is to discuss a class of semilinear fractional integro-differential equations in fractional power spaces. By using fractional calculus theory, \(\alpha \) α -resolvent operators, the Banach fixed point theorem and a generalized Gronwall inequality, we first study the existence and uniqueness of solutions for Cauchy problems. Meanwhile, the continuous dependence and \(\epsilon \) ϵ -continuous dependence of solutions on the initial condition are discussed. In addition, we introduce a new concept of h-Mittag-Leffler-Ulam’s type stability, and obtain the results of this type stability for the considered equations on a compact interval. Eventually, an example illustrates our results.