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<p>This work establishes the approximate controllability of nonlinear Hadamard-type fractional systems with weakly singular logarithmic kernels in Banach spaces. Under suitable assumptions on the linearized control operator and a linear growth condition on the nonlinearity, we prove the existence of a mild solution steering the system from an arbitrary initial state arbitrarily close to a prescribed terminal state. The proof combines Krasnoselskii’s fixed point theorem with refined estimates involving logarithmic convolutions.</p>

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Existence and Approximate Controllability of Mild Solutions for Hadamard-Type Fractional Systems in Banach Spaces

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Fatima Mesri,
  • Thabet Abdeljawad

摘要

This work establishes the approximate controllability of nonlinear Hadamard-type fractional systems with weakly singular logarithmic kernels in Banach spaces. Under suitable assumptions on the linearized control operator and a linear growth condition on the nonlinearity, we prove the existence of a mild solution steering the system from an arbitrary initial state arbitrarily close to a prescribed terminal state. The proof combines Krasnoselskii’s fixed point theorem with refined estimates involving logarithmic convolutions.