In this paper, a deep learning optimization algorithm is proposed, which based on the Grünwald–Letnikov (G-L) fractional order definition. An optimizer calculus gradient descent G-L definition (FCGD_G-L) designed. Using short-memory effect of definition, derivation only needs 10 time steps. At same time, via transforming formula Gamma function eliminated. Thereby, it can achieve unification and...

Povzetek. V članku predstavljava razširjenost obremenjujočih in pozitivnih izkušenj v otroštvu (OIO PIO) na panelnem (pod)vzorcu 18- do 30-letnikov/-ic Sloveniji ter njihovo povezanost s samoocenjenim šolskim uspehom. Skoraj petina 30-letnikov iz prve slovenske OIO-raziskave je poročala o podpovprečnem šolskem uspehu 18. leta starosti. Skladno predhodnimi študijami so takem pogosteje poročali t...

This paper presents a novel adaptive fuzzy logic controller (FLC) equipped with an adaptive algorithm to achieve synchronization performance for fractional chaotic systems. By introducing the fuzzy control design and robustness tracking approach, a desired synchronization error can be attenuated to a prescribed level, even in the presence of the high level of uncertainties and noisy training da...

Abstract In the continuous-time random walk model, time-fractional operator usually expresses an infinite waiting time probability density. Different from that usual setting, this work considers tempered operator, which reflects a finite Firstly, we analyse solution of benchmark problem, shows weak singularity near initial time. The L1 scheme on graded mesh and weighted shifted Grünwald–Letniko...

System identification is important in science and engineering. This contribution proposes a simple yet elegant scheme for identifying a fractional order dynamic system based on its observed response to a standard excitation. Our approach consists in obtaining and solving a set of simultaneous linear equations connecting the parameters to yield the desired estimates. To minimise the effect of no...

This paper introduces a numerical technique for the estimation of stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise excitation. The Wiener-Hermite expansion is integrated with the Grunwald-Letnikov approximation in case of fractional order damping and with Coimbra approximation in case of variableorder damping. The numerical solver...

In this survey paper, we analyze the development of Fractional Calculus in Russia at end XIX century, particular, results by A. V. Letnikov, N. Ya. Sonine, and P. Nekrasov. Some discussed are either unknown or inaccessible.