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5 demonstrate that: (i) coefficient I u i HT ht increases as HT ht is increased and I u i HT ht approaches 2 as I M i approaches 3. If I M i is an irrational number or it leads to the occurrence of a recurring decimal for HT ht , then HT ht may be truncated to three digits after the decimal point (viz., I H i ( I s i ) for I M i = 2.5, 2.8). Various approaches have been reported to emulate the frequency response of HT ht , [[5]]. [Extracted from the article]

This paper presents a new approach for reduction of commensurate fractional-order single-input-single-output systems. The minimization in the frequency response error of the reduced order model (ROM) relative to the original system is carried out in the F-plane. A constrained optimization technique is introduced to satisfy the angle criteria for F-domain stability of the proposed ROM. Significant improvements in both the time- and frequency-responses over the recently published literature are illustrated using several numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, a recently proposed metaheuristic optimization technique called hybrid flower pollination algorithm (HFPA) is applied to design wideband infinite impulse response digital differentiators (DDs) and digital integrators (DIs). In recent years, benchmark nature-inspired optimization algorithms such as particle swarm optimization (PSO), simulated annealing, and genetic algorithm have been employed for the design of wideband DDs and DIs. However, individually, these algorithms show major drawbacks such as premature convergence, thus leading to a sub-optimal solution. HFPA, however, is a hybrid approach which combines the efficient exploitation and exploration capabilities of two different metaheuristics, namely PSO and flower pollination algorithm (FPA), respectively. The HFPA-based designs have been compared with real-coded genetic algorithm, PSO, differential evolution, success-history-based adaptive differential evolution with linear population size reduction (L-SHADE), self-adaptive differential evolution (jDE), and FPA-based designs with respect to the solution quality, robustness, convergence, and optimization time. Simulation results demonstrate that among all the algorithms, the HFPA-based designs consistently achieve superior performances in the least number of function evaluations. Exhaustive experimentations are conducted to determine the best values of the control parameters of HFPA for the optimal design of DDs and DIs. The proposed designs also outperform the recently reported designs based on non-optimal, classical, and nature-inspired optimization approaches in terms of magnitude response. The lower orders of the proposed designs render them suitable for real-time applications. [ABSTRACT FROM AUTHOR]

B Publisher Correction: Fractional Calculus and Applied Analysis (2023) 26:1566-1593 b https://doi.org/10.1007/s13540-023-00168-x The original online version of this article was revised: Figure 6 was replaced with Figure 7, making Figure 7 serve for both 6 and 7. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. [Extracted from the article]