We consider the distributed-order space-time fractional heat type equation \begin{document}$ \mathbb{D}^{(\nu)}u(t, x) = -(-\Delta)^{\alpha/2}u(t, x), \ t>0, x\in D, $\end{document} where$ \mathbb{D}^{(\nu)} $ is derivative based on Caputo time-fractional derivative, -(-\Delta)^{\alpha/2} generator of an isotropic stable process for \alpha\in(0, 2] $, D a bounded domain in \mathbb{R}^d and \...

As an important field of Distributed artificial intelligence (DAI), multi-agent systems (MASs) have attracted the attention extensive research scholars. Consensus as most issue in MAS, much progress has been made studying consensus control but there are some problems remained largely unaddressed which cause MAS to lose useful network structure information. First, protocol usually proceeds over ...

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In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing a new operator. This derivative combines two known operators: respect to another function. The main results of paper are necessary sufficient optimality conditions for different types problems. Since generalized derivatives, from some well-known can be obtained as partic...