Fractional operator without singular kernel: Applications to linear electrical circuits

Morales‐Delgado, V. F.; Gómez-Aguilar, J. F.; Taneco-Hernández, M.A.; Escobar-Jiménez, R.F.

doi:10.1002/cta.2564

Cited by 33 publications

(14 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, with zero initial conditions, both derivatives are identical, a property already known from the classical Riemann-Liouville and Caputo-Liouville derivatives [118]. Modelling with Atangana-Baleanu derivative is a hot topic in the contemporary literature focusing on various natural problems [11,12,16,45,47,88,107,143], but our task now is to demonstrate its appearance in the constitutive equations of the linear viscoelasticity of solid (viscoelastic fluids are not discussed here but this will be a special task in the future).…”

Section: Riemann-liouville Sense (Abr Derivative)mentioning

confidence: 99%

Response functions in linear viscoelastic constitutive equations and related fractional operators

Hristov

2019

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

This study addresses the stress–strain relaxation functions of solid polymers in the framework of the linear viscoelasticity with aim to establish the adequate fractional operators emerging from the hereditary integrals. The analysis encompasses power-law and non-power-law materials, thus allowing to see the origins of application of the tools of the classical fractional calculus with singular memory kernels and the ideas leading towards fractional operators with non-singular (regular) kernels. A step ahead in modelling with hereditary integrals is the decomposition of non-power-law relaxation curves by Prony series, thus obtaining discrete relaxation kernels with a finite number of terms. This approach allows for seeing the physical background of the newly defined Caputo–Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories. The non-power-law relaxation curves also allow for approximations by the Mittag–Leffler function of one parameter that leads reasonably into stress–strain hereditary integrals in terms of Atangana–Baleanu fractional derivative of Caputo sense. The main outcomes of the analysis done are the demonstrated distinguishes between the relaxation curve behaviours of different materials and are therefore the adequate modelling with suitable fractional operators.

show abstract

Section: Riemann-liouville Sense (Abr Derivative)mentioning

confidence: 99%

Response functions in linear viscoelastic constitutive equations and related fractional operators

Hristov

2019

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

show abstract

“…with variable τ α being the time-constant, associated to the pole frequency (ω 0 ) through the relationship: (1), the expressions of the gain and phase responses are given by (2) and (3), respectively…”

Section: Fractional-order Filtersmentioning

confidence: 99%

“…Owing to the interdisciplinary nature of fractional-order calculus [1][2][3], the development of fractional-order filters has gained a significant research interest because of the offered more precise gradient of the transition from pass-band to stop-band, with regards to their integer-order counterparts. This originates from the fact that the slope of the attenuation of an n + α order filter, with n integer and 0 < α < 1, is equal to −6 · (n + α) dB/Oct., instead of −6 · n dB/Oct.…”

Section: Introductionmentioning

confidence: 99%

Minimum MOS Transistor Count Fractional-Order Voltage-Mode and Current-Mode Filters

et al. 2019

View full text Add to dashboard Cite

Voltage-mode and current-mode fractional-order filter topologies, which are capable of realizing various types of transfer functions, are introduced in this paper. Thanks to the employment of the transconductance parameter of the MOS transistors, the derived filter structures offer the benefit of the electronic adjustment of their frequency characteristics. With regards to the literature, the number of MOS transisitors is minimized leading to significant reduction of the circuit complexity and power dissipation. Simulation results, derived using the Design Kit of the 0.35 μm Austria Mikro Systeme CMOS process and the Cadence IC design suite, confirm the correct operation of the presented filter structures.

show abstract

“…Fractional calculus has received much attraction over this last decade and grew many papers with many applications in sciences and engineering [1,2], in mathematical physics [3,4], in physics [3,5], biology [6], and many other fields of sciences [7]. There exist, in our opinion, many interesting works on the application of fractional calculus in the literature; the authors of the following investigations [8,9] can be considered references in fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Algorithm Applied to Free Convection Flows of the Casson Fluid along with Heat and Mass Transfer Described by the Caputo Derivative

Sene

2021

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this paper, we present a class of numerical schemes and apply it to the diffusion equations. The objective is to obtain numerical solutions of the constructive equations of a type of Casson fluid model. We investigate the solutions of the free convection flow of the Casson fluid along with heat and mass transfer in the context of modeling with the fractional operators. The numerical scheme presented in this paper is called the fractional version of the Adams Basford numerical procedure. The advantage of this numerical technique is that it combines the Laplace transforms and the classical Adams Basford numerical procedure. Note that the usage of the Laplace transforms makes possible the applicability of the numerical approach to diffusion equations in general. The Caputo derivative will be used in the investigations. The influence of the considered Casson fluid model parameters as the Prandtl number Pr , the Schmidt number Sc , the material parameter of the Casson fluid β , and the order of the Caputo fractional derivative on the dynamics of the temperature, concentration, and velocity profiles has been presented analyzed. Graphical representations have supported the results of the paper.

show abstract

Fractional operator without singular kernel: Applications to linear electrical circuits

Cited by 33 publications

References 34 publications

Response functions in linear viscoelastic constitutive equations and related fractional operators

Response functions in linear viscoelastic constitutive equations and related fractional operators

Minimum MOS Transistor Count Fractional-Order Voltage-Mode and Current-Mode Filters

A Numerical Algorithm Applied to Free Convection Flows of the Casson Fluid along with Heat and Mass Transfer Described by the Caputo Derivative

Contact Info

Product

Resources

About