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<p>This paper studies the controllability of complex networks governed by nonlinear <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>-fractional differential equations. Using a generalized Caputo-type derivative with respect to an increasing function <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>, the model captures memory effects and nonlocal temporal dynamics beyond classical fractional systems. Sufficient conditions for the controllability of both linear and nonlinear networks are established via semigroup theory and fixed-point techniques. The results highlight the influence of network topology and the properties of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation> on the reachable set and control performance. Numerical simulations illustrate the applicability of the theoretical findings. The proposed framework generalizes existing fractional controllability results and provides a foundation for controlling complex dynamical networks with memory effects.</p>

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Controllability criteria for nonlinear fractional dynamical networks in Banach spaces

  • 期刊论文

  • 发表日期：

    2026年7月26日

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  • Youssef Afdifid,
  • Ali El Mfadel,
  • M.’hamed Elomari

摘要

This paper studies the controllability of complex networks governed by nonlinear \(\varphi \) φ -fractional differential equations. Using a generalized Caputo-type derivative with respect to an increasing function \(\varphi \) φ , the model captures memory effects and nonlocal temporal dynamics beyond classical fractional systems. Sufficient conditions for the controllability of both linear and nonlinear networks are established via semigroup theory and fixed-point techniques. The results highlight the influence of network topology and the properties of \(\varphi \) φ on the reachable set and control performance. Numerical simulations illustrate the applicability of the theoretical findings. The proposed framework generalizes existing fractional controllability results and provides a foundation for controlling complex dynamical networks with memory effects.