Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by distributed-order equations. In the present paper we consider different forms of distributed-order fractional kinetic equations and investigate the effects descri...

Distributed First Order Logic (DFOL) is a formalism introduced more than 10 years ago with the purpose of formalising distributed knowledge-based systems. In these systems, knowledge is scattered in a set of heterogeneous and interconnected modules. The original version of DFOL defined a set of primitives for the specification of a restricted subset of interconnections between knowledge modules...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

We present the first specification and verification of an implementation a causally-consistent distributed database that supports modular full functional correctness properties clients servers. specify reason about in Aneris, higher-order separation logic for ML-like programming language with network primitives systems. demonstrate our specifications are useful, by proving small, but tricky, sy...

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove strong necessary optimality condition of Pontryagin type. The possibility that admissible are subject to pointwise constraints is new requires more sophisticated techniques include maximality condition. start by proving results continuity solutions due needle-like pe...