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<p>This paper presents a systematic study of mild nonnegative solutions for iterative Caputo fractional totally nonlinear differential equations. First, we transform the differential equation into an integral formulation using the Laplace and inverse Laplace transform techniques. This reformulation enables us to rigorously investigate the fundamental properties of mild nonnegative solutions, including their existence, uniqueness and continuous dependence, as well as their Ulam-type stability. Leveraging the Krasnoselskii, Burton-Krasnoselskii and Banach fixed-point theorems, we establish novel existence and uniqueness results under appropriate conditions. To validate our theoretical findings, we conclude with two concrete examples that prove the applicability of the results.</p>

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Qualitative properties of iterative fractional totally nonlinear differential equations

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Mohammed Messous,
  • Abdelouaheb Ardjouni

摘要

This paper presents a systematic study of mild nonnegative solutions for iterative Caputo fractional totally nonlinear differential equations. First, we transform the differential equation into an integral formulation using the Laplace and inverse Laplace transform techniques. This reformulation enables us to rigorously investigate the fundamental properties of mild nonnegative solutions, including their existence, uniqueness and continuous dependence, as well as their Ulam-type stability. Leveraging the Krasnoselskii, Burton-Krasnoselskii and Banach fixed-point theorems, we establish novel existence and uniqueness results under appropriate conditions. To validate our theoretical findings, we conclude with two concrete examples that prove the applicability of the results.