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In this work, we study the existence of solutions of nonlinear fractional coupled system of $\varphi $-Hilfer type in the frame of Banach spaces. We improve a property of a measure of noncompactness in a suitably selected Banach space. Darbo’s fixed point theorem is applied to obtain a new existence result. Finally, the validity of our result is illustrated through an example.

Synchronisation is one of the most interesting collective motions observed in large-scale complex networks of interacting dynamical systems. We consider global synchronisation for networks of nonlinearly coupled identical cells with time delays, using an approach where the synchronisation problem is converted to solving an homogeneous linear system. This approach is extended to fit networks under more general coupling topologies, and we derive four delay-dependent and delay-independent criteria that ensure the coupled dynamical network is globally synchronised. Some examples show that the four criteria are not mutually inclusive, and numerical simulations also demonstrate our theoretical results.

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Theoretical study of a $\varphi $-Hilfer fractional differential system in Banach spaces

Further Analysis of Global Synchronisation for Networks of Identical Cells with Delayed Coupling

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2 results

Theoretical study of a $\varphi $-Hilfer fractional differential system in Banach spaces

Further Analysis of Global Synchronisation for Networks of Identical Cells with Delayed Coupling