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<p>In this manuscript, sufficient conditions for the existence and uniqueness of solutions to the Hilfer-Katugampola Fractional Differential Equations, characterized by two parameters, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varkappa \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϰ</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varsigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ς</mi> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\varsigma \le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ς</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varkappa &gt; 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϰ</mi> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>), which generalize classical fractional differential equations are established. By a fixed point technique and the results of fractional calculus, the local asymptotic stability of the attractive solution is analyzed. Two numerical examples are provided in order to illustrate the attractivity results.</p>

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Attractivity and Asymptotic Stability in Hilfer-Katugampola Fractional Differential Equations

  • 期刊论文

  • 发表日期：

    2026年2月21日

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  • Prabha Arunagiri,
  • Nirmalkumar Rajendran,
  • Prasantha Bharathi Dhandapani,
  • Carlos Martin-Barreiro,
  • Xavier Cabezas

摘要

In this manuscript, sufficient conditions for the existence and uniqueness of solutions to the Hilfer-Katugampola Fractional Differential Equations, characterized by two parameters, \(\varkappa \) ϰ and \(\varsigma \) ς ( \(\varsigma \le 1\) ς ≤ 1 and \(\varkappa > 1\) ϰ > 1 ), which generalize classical fractional differential equations are established. By a fixed point technique and the results of fractional calculus, the local asymptotic stability of the attractive solution is analyzed. Two numerical examples are provided in order to illustrate the attractivity results.