A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication 20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515

On Finite Noncommutativity in Quantum Field Theory

We consider various modifications of the Weyl-Moyal star-product, in order to obtain a finite range of nonlocality. The basic requirements are to preserve the commutation relations of the coordinates as well as the associativity of the new product. We show that a modification of the differential representation of the Weyl-Moyal star-product by an exponential function of derivatives will not lead to a finite range of nonlocality. We also modify the integral kernel of the star-product introducing a Gaussian damping, but find a nonassociative product which remains infinitely nonlocal. We are therefore led to propose that the Weyl-Moyal product should be modified by a cutoff like function, in order to remove the infinite nonlocality of the product. We provide such a product, but it appears that one has to abandon the possibility of analytic calculation with the new product.Comment: 13 pages, reference adde

Dynamical noncommutativity

We present a model of Moyal-type noncommutativity with time-depending noncommutativity parameter and the exact gauge invariant action for the U(1) noncommutative gauge theory. We briefly result the results of the analysis of plane-wave propagation in a regime of a small but rapidly changing noncommutativity.Comment: 10 pages, JHEP styl

(SI10-115) Controllability Results for Nonlinear Impulsive Functional Neutral Integrodifferential Equations in n-Dimensional Fuzzy Vector Space

In this paper, we concentrated to study the controllability of fuzzy solution for nonlinear impulsive functional neutral integrodifferential equations with nonlocal condition in n-dimensional vector space. Moreover, we obtained controllability of fuzzy result for the normal, convex, upper semi-continuous and compactly supported interval fuzzy number. Finally, an example was provided to reveal the application of the result

Existence of solutions to uncertain differential equations of nonlocal type via an extended Krasnosel’skii fixed point theorem

In the present study, we investigate the existence of the solutions to a type of uncertain differential equations subject to nonlocal derivatives. The approach is based on the application of an extended Krasnosel’skii fixed point theorem valid on fuzzy metric spaces. With this theorem, we deduce that the problem of interest has a fuzzy solution, which is defined on a certain interval. Our approach includes the consideration of a related integral problem, to which the above-mentioned tools are applicable. We finish with some physical motivationsWe are grateful to the Editor and the anonymous Referees for their comments and suggestions that helped to improve the paper. The research of J.J.N. and R.R.L. is supported by grant numbers PID2020-113275GB-I00 (AEI/FEDER, UE), MTM2016-75140-P (AEI/FEDER, UE), and ED431C 2019/02 (GRC Xunta de Galicia). The visit of A.K. to the University of Santiago de Compostela has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain, co-financed by the European Fund for Regional Development (FEDER) corresponding to the 2014-2020 multiyear financial framework, project MTM2016-75140-P; and by Xunta de Galicia under grant ED431C 2019/02. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer NatureS