scholarly journals Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory

2020 ◽  
Vol 8 ◽  
Author(s):  
Harendra Singh ◽  
H. M. Srivastava
Keyword(s):  
Numerical Investigation ◽  
Fractional Order ◽  
Circuit Theory ◽  
Duffing Equations

Modeling and numerical investigation of fractional‐order bovine babesiosis disease

2020 ◽  
Author(s):  
Aqeel Ahmad ◽  
Muhammad Farman ◽  
Parvaiz Ahmad Naik ◽  
Nayab Zafar ◽  
Ali Akgul ◽  
...  
Keyword(s):  
Numerical Investigation ◽  
Fractional Order ◽  
Bovine Babesiosis

Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach

2016 ◽  
Vol 22 (3) ◽  
pp. 773-782 ◽  
Author(s):  
Khaled Moaddy ◽  
Asad Freihat ◽  
Mohammed Al-Smadi ◽  
Eman Abuteen ◽  
Ishak Hashim
Keyword(s):  
Numerical Investigation ◽  
Fractional Order

scholarly journals On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory

Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5768 ◽  
Author(s):  
Jacek Gulgowski ◽  
Tomasz P. Stefański ◽  
Damian Trofimowicz
Keyword(s):  
Transmission Line ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Circuit Theory ◽  
Base Point ◽  
Semigroup Property ◽  
Caputo Derivatives ◽  
Potential Problems ◽  
Limited Applicability

In this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited applicability in the circuit theory. Out of the most popular approaches considered in this paper, only the Grünwald–Letnikov and Marchaud definitions (which are actually equivalent) satisfy the semigroup property and are naturally representable in the phasor domain. The generalization of this concept, i.e., the two-sided fractional Ortigueira–Machado derivative, satisfies the semigroup property, but its phasor representation is less natural. Other ideas (including the Riemann–Liouville and Caputo derivatives—with a finite or an infinite base point) seem to have limited applicability.

scholarly journals Theoretical Verification of Formula for Charge Function in Time q = c * v in RC Circuit for Charging/Discharging of Fractional & Ideal Capacitor

2019 ◽  
pp. 1-39
Author(s):  
Shantanu Das
Keyword(s):  
Memory Effect ◽  
Fractional Order ◽  
Circuit Theory ◽  
Charge Storage ◽  
Fractional Ideal ◽  
History Of ◽  
Rc Circuit ◽  
New Formulation ◽  
New Formula ◽  
Super Capacitors

Objective of this paper is verification of newly developed formula of charge storage in capacitor as   q = c*v, in RC circuit, to get validation for ideal loss less capacitor as well as fractional order capacitors for charging and discharging cases. This new formula is different to usual and conventional way of writing capacitance multiplied by voltage to get charge stored in a capacitor   i.e. q = cv. We use this new formulation i.e.   q = c*v in RC circuits to verify the results that are obtained via classical circuit theory, for a case of classical loss less capacitor as well as fractional capacitor. The use of this formulation is suited for super-capacitors, as they show fractional order in their behavior. This new formula is used to get the ‘memory effect’ that is observed in self-discharging phenomena of super-capacitors-that memorizes its history of charging profile. Special emphasis is given to detailed derivational steps in order to clarity in usage of this new formula in the RC circuit examples. This paper validates  the new formula of   charge   storage  in  capacitor i.e. q = c*v.

scholarly journals Numerical investigation of fractional-order unsteady natural convective radiating flow of nanofluid in a vertical channel

2019 ◽  
Vol 4 (5) ◽  
pp. 1416-1429 ◽  
Author(s):  
Muhammad Hamid ◽  
◽  
Tamour Zubair ◽  
Muhammad Usman ◽  
Rizwan Ul Huq ◽  
...  
Keyword(s):  
Numerical Investigation ◽  
Fractional Order ◽  
Vertical Channel
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