Analytical studies for linear periodic systems of fractional order

Rezazadeh, Hadi; Aminikhah, Hossein; Sheikhani, A. H. Refahi

doi:10.1007/s40096-015-0172-7

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…Rezazadeh et al recently examined the stability of Hilfer fractional differential equations system by using the properties of Mittag-Leffler functions [14]. In [15], the authors studied the stability for the fractional Floquet system and shown the fractional Floquet system is asymptotically stable if all multipliers have real parts between -1 and 1.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of linear conformable fractional differential equations system with time delays

Mohammadnezhad

Eslami

Rezazadeh

2019

bspm

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In this paper, we first study stability analysis of linear conformable fractional differential equations system with time delays. Some sufficient conditions on the asymptotic stability for these systems are proposed by using properties of the fractional Laplace transform and fractional version of final value theorem. Then, we employ conformable Euler’s method to solve conformable fractional differential equations system with time delays to illustrate the effectiveness of our theoretical results

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Section: Introductionmentioning

confidence: 99%

Stability analysis of linear conformable fractional differential equations system with time delays

Mohammadnezhad

Eslami

Rezazadeh

2019

bspm

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“…The following results give the stability analysis of such a system. [66,67] Theorem 1. A commensurate order system (39) is stable if the following condition is met:…”

Section: Stability Analysismentioning

confidence: 99%

Modified fractional order PID structure for non‐integer model bioreactor control

Maurya,

Paul,

Prasad

et al. 2024

Can J Chem Eng

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Temperature control for fermentation is crucial as it directly affects microorganism growth, productivity, and metabolic activity. This work proposes a modified fractional order proportional‐integral‐derivative (FOPID‐DF) controller that incorporates the system model in the control loop configuration utilizing a differential filter for precise temperature control within a narrow operating range. PID, fractional order PID (FOPID), modified fractional order PID (MFOPID), and fractional order internal model control (IMC) controllers were also designed for comparative analysis. The simulation results demonstrated that the proposed FOPID‐DF controller outperforms the other designed controllers, shown by a 22.33% reduction in integral absolute error (IAE) and a 29.06% decrease in integral square error (ISE) compared to the FOPID controller and various other improved performance indicators. Parameter variation and noise analysis highlighted the ability of the controller to maintain stability and performance under changing conditions. The simulation outcomes suggested that the FOPID‐DF controller excels in temperature control, ensuring optimal microorganism growth and metabolic activity.

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“…The fractional derivative proposed by Hilfer yields Caputo (µ = 1) and Riemann Liouville derivative (µ = 0) as particular cases. Some recent works on fractional order Hilfer derivatives can be found in [13][14][15][16][17][18]. Perturbation techniques are powerful tools in nonlinear analysis for studying diverse aspects of the solution of nonlinear dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

A Study of Generalized Hybrid Discrete Pantograph Equation via Hilfer Fractional Operator

et al. 2022

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Pantograph, a device in which an electric current is collected from overhead contact wires, is introduced to increase the speed of trains or trams. The work aims to study the stability properties of the nonlinear fractional order generalized pantograph equation with discrete time, using the Hilfer operator. Hybrid fixed point theorem is considered to study the existence of solutions, and the uniqueness of the solution is proved using Banach contraction theorem. Stability results in the sense of Ulam and Hyers, and its generalized form of stability for the considered initial value problem are established and we depict numerical simulations to demonstrate the impact of the fractional order on stability.

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Analytical studies for linear periodic systems of fractional order

Cited by 7 publications

References 18 publications

Stability analysis of linear conformable fractional differential equations system with time delays

Stability analysis of linear conformable fractional differential equations system with time delays

Modified fractional order PID structure for non‐integer model bioreactor control

A Study of Generalized Hybrid Discrete Pantograph Equation via Hilfer Fractional Operator

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