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<p>The current study discusses boundary value problems of nonlinear fractional integro-differential equations with Riemann-Caputo derivatives. Some new existence and uniqueness results are proposed by using the Banach contraction principle and Krasnosel’skii fixed point theorems. Furthermore, some sufficient conditions are given to estimate the existence of integrable solution in <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>P</mi> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{P}$</EquationSource> </InlineEquation> spaces. Also, we make use the Ulam-Hyers stability for the given problem to derive the desired results. Finally, an illustrative example is studied to support the obtained results.</p>

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Solution of fractional integro-differential equations with some existence and stability results

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月15日

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  • Chahra Kechar,
  • Ahmed A. Hamoud,
  • Abdelouaheb Ardjouni,
  • Homan Emadifar,
  • Karim K. Ahmed

摘要

The current study discusses boundary value problems of nonlinear fractional integro-differential equations with Riemann-Caputo derivatives. Some new existence and uniqueness results are proposed by using the Banach contraction principle and Krasnosel’skii fixed point theorems. Furthermore, some sufficient conditions are given to estimate the existence of integrable solution in L P $L^{P}$ spaces. Also, we make use the Ulam-Hyers stability for the given problem to derive the desired results. Finally, an illustrative example is studied to support the obtained results.