Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls

In this paper, we mainly consider a control system governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. We first establish sufficient conditions for the existence of mild solutions to the addressed control system via properties of generalized Clarke subdifferential and a fixed point theorem for condensing multivalued maps. Then we present the existence of optimal state-control pairs of the limited Lagrange optimal systems governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. The optimal control results are derived without uniqueness of solutions for the control system

Existence results for dynamic inclusions on time scales with nonlocal initial conditions

AbstractThis paper is mainly concerned with the existence of solutions for first order dynamic inclusions on time scales with nonlocal initial conditions. By using Bohnenblust–Karlin’s fixed point theorem and Leray–Schauder nonlinear alternative for multivalued maps, some sufficient conditions are established. An example is also included to illustrate our results

Global existence and controllability to a stochastic integro-differential equation

In this paper, we are focused upon the global uniqueness results for a stochastic integro-differential equation in Fréchet spaces. The main results are proved by using the resolvent operators combined with a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. As an application, a controllability result with one parameter is given to illustrate the theory

Asymptotic behavior of solutions to abstract stochastic fractional partial integrodifferential equations

The existence of asymptotically almost automorphic mild solutions to an abstract stochastic fractional partial integrodifferential equation is considered. The main tools are some suitable composition results for asymptotically almost automorphic processes, the theory of sectorial linear operators, and classical fixed point theorems. An example is also given to illustrate the main theorems.The first author was supported by Research Fund for Young Teachers of Sanming University (B2011071Q). The second author was supported by NSF of China (11361032), Program for New Century Excellent Talents in University (NCET-10-0022), and NSF of Gansu Province of China (1107RJZA091). And the third author was partially supported by Ministerio de Economia y Competitividad (Spain), project MTM2010-15314, and cofinanced by the European Community fund FEDER.S

Pseudo almost automorphic behavior of solutions to a semi-linear fractional differential equation

In this paper, we shall deal with $mu$-pseudo almost automorphic solutions to a semi-linear fractional differential equation by new concept of $mu$-pseudo almost automorphic functions presented recently. We first establish some new properties of $mu$-pseudo almost automorphic functions, and then we apply the results obtained to prove some existence theorems combined with the Leray-Schauder alternative theorem

Research Article

Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to a partial functional differential equation in Banach space

Development of a flexible rogowski coil sensor for partial discharge detection in power cables

Partial discharge (PD) is a prevalent problem in power cables that must be detected early to avert power outages and ensure system reliability. Despite the fact that numerous Rogowski coil (RC) designs, none of them can accommodate all cable sizes. The purpose of this research is to investigate the sensitivity of flexible RC sensors and develop a prototype that uses Thermoplastic Polyurethane (TPU) for enhanced flexibility and accuracy. This study emphasizes the significance of flexible RC sensors in early PD detection for enhanced flexibility and potential benefits for power system monitoring and maintenance. The RC construction is designed in AutoCAD and 3D printed in TPU. The RC is wound with 20 turns and employs a return loop method to reduce interference from external electromagnetic fields. According to experimental validation, the sensor sensitivity is directly proportional to the greatest amplitude of the recorded PD signal, demonstrating the potential to improve power system dependability and safety through early PD detection. These findings highlight the need to consider the PD signal's maximum amplitude for sensor sensitivity, ultimately adding to the power system's reliability and safety. The proposed design, characterized by its novelty with TPU materials, yields promising results in terms of flexibility, establishing flexible RC sensors as a feasible asset in power cable PD detection and boosting monitoring and maintenance practice

D-wave Charmonium Production in e+e−e^+e^- Annihilation at s=10.6\sqrt{s}=10.6 GeV

We calculate the D-wave charmonium production in $e^+e^-$ annihilation at BELLE and BABAR at $\sqrt{s}=10.6$ GeV using the nonrelativistic QCD factorization formalism, including color singlet and color octet contributions. We analyze the contributions of various processes for $\delta_J(J=1,2)$ production. We find that both the color singlet and color octet channels may give substantial contributions, and the production rates are estimated to be $\sigma (\delta_1)\simeq 0.043-0.16pb$ and $\sigma (\delta_2)\simeq 0.094-0.29pb$, which, however, are very sensitive to the choice of the color octet matrix elements of the D-wave charmonium states. The measurement of D-wave charmonium production at BABAR and BELLE in the future will be very helpful to test the color octet mechanism and to determine the color octet matrix elements.Comment: 9 pages, 1 figure, final version to appear in Physics Letters