A numerical study of new fractional model for convective straight fin using fractional-order Legendre functions

Sharma, Sunil Kumar; Kumar, Dinesh

doi:10.1016/j.chaos.2020.110282

Cited by 10 publications

(3 citation statements)

References 27 publications

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“…However, fractional functions are used to solve this limitation. For instance, see previous studies 12–16 …”

Section: Introductionmentioning

confidence: 98%

“…For instance, see previous studies. [12][13][14][15][16] The Müntz-Legender functions (MLFs) are orthogonal and fractional functions which for the first time introduced and employed in Borwein et al, 17 McCarthy et al, 18 and Milovanovi ć. 19 In recent years, these functions have been successfully applied for various problems, such as delay fractional optimal control problems, 20 fractional Volterra-Fredholm integro-differential equations, 21 fractional differential equations, [22][23][24] Volterra-Fredholm integral equations, 25 Bagley-Torvik equation, 26 and fractional partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

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A hybrid approach established upon the Müntz‐Legender functions and 2D Müntz‐Legender wavelets for fractional Sobolev equation

Hosseininia

Heydari

Avazzadeh

2022

Math Methods in App Sciences

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This article proposes a hybrid technique for finding approximation solutions of the fractional 2D Sobolev equation. In the proposed approach, the Müntz-Legender functions and Müntz-Legender wavelets are, respectively, utilized to approximate the solution of the problem under consideration in the time and spatial directions. By implementing the presented technique, solving the 2D fractional Sobolev equation is converted into solving a system of algebraic equations. Three examples are solved to examine the validity of the proposed method.

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“…However, fractional functions are used to solve this limitation. For instance, see previous studies 12–16 …”

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

A hybrid approach established upon the Müntz‐Legender functions and 2D Müntz‐Legender wavelets for fractional Sobolev equation

Hosseininia

Heydari

Avazzadeh

2022

Math Methods in App Sciences

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“…In control engineering, fractional calculus has been used widely for systems modeling, observers designing, and the design of controllers. Although it is not a new theory, it has been used to characterize real-world systems without complicating their existing models, as shown in [5][6][7][8][9][10]. Tese works are focused on using continuous time-fractional defnitions.…”

Section: Introductionmentioning

confidence: 99%

Sensor FDI System Based on Discrete‐TimeFractional‐Order Observers

Escobar-Jiménez

Alegría-Zamudio

Téllez-Anguiano

et al. 2023

Mathematical Problems in Engineering

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The design of sensor fault detection and isolation (FDI) systems has been studied widely by several authors of different fields of science (engineering, mathematics, physics) to ensure the continuous operation of systems or processes. This research presents the design and evaluation of a fault detection and isolation (FDI) system based on discrete fractional-orderhigh-gain observers (DFOHGO) for the outlet temperature sensors of a heat exchanger. The formulation of the discrete fractional-order observers is based on the Grünwald–Letnikov fractional-order derivative. The FDI system is based on a bank of two DFOHGOs to carry out a residual evaluation. The obtained results showed that the DFOHGOs provide accurate estimations of the temperatures. This allows switching the faulty sensor signal to the temperature estimations provided by the DFOHGOs when a fault occurs.

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Taylor–Galerkin–Legendre-wavelet approach to the analysis of a moving fin with size-dependent thermal conductivity and temperature-dependent internal heat generation

Chaurasiya,

Upadhyay,

Rai

et al. 2023

J Therm Anal Calorim

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A numerical study of new fractional model for convective straight fin using fractional-order Legendre functions

Cited by 10 publications

References 27 publications

A hybrid approach established upon the Müntz‐Legender functions and 2D Müntz‐Legender wavelets for fractional Sobolev equation

A hybrid approach established upon the Müntz‐Legender functions and 2D Müntz‐Legender wavelets for fractional Sobolev equation

Sensor FDI System Based on Discrete‐TimeFractional‐Order Observers

Taylor–Galerkin–Legendre-wavelet approach to the analysis of a moving fin with size-dependent thermal conductivity and temperature-dependent internal heat generation

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