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<p>This research focuses on a detailed investigation of the existence and uniqueness of solutions to nonlocal value problems for fractional integro-differential evolution systems involving a <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>-Caputo derivative. Specifically, we derive the solution formula in terms of the semigroup generated by the resolvent and the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>-function associated with the Caputo fractional derivative, using the generalized Laplace transform method with the aid of certain probability density functions. To establish the existence of solutions, we utilize Mönch’s fixed point theorem, while Banach’s fixed point theorem is employed to confirm uniqueness. Finally, we illustrate the main results and their implications within the context of semigroups and fractional derivatives using two concrete examples.</p>

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EXISTENCE AND UNIQUENESS ANALYSIS OF \(\varphi \)-CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS USING MEASURES OF NONCOMPACTNESS

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • A. Taqbibt,
  • N. Chefnaj,
  • K. Hilal,
  • M. Elomari

摘要

This research focuses on a detailed investigation of the existence and uniqueness of solutions to nonlocal value problems for fractional integro-differential evolution systems involving a \(\varphi \) φ -Caputo derivative. Specifically, we derive the solution formula in terms of the semigroup generated by the resolvent and the \(\varphi \) φ -function associated with the Caputo fractional derivative, using the generalized Laplace transform method with the aid of certain probability density functions. To establish the existence of solutions, we utilize Mönch’s fixed point theorem, while Banach’s fixed point theorem is employed to confirm uniqueness. Finally, we illustrate the main results and their implications within the context of semigroups and fractional derivatives using two concrete examples.