Fractional derivative of logarithmic function and its applications as multipurpose ASP circuit

Mishra, Shalabh Kumar; Gupta, Maneesha; Upadhyay, Dharmendra Kumar

doi:10.1007/s10470-018-1328-9

Cited by 7 publications

(4 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Observe that the left-hand side of the above system is the Caputo fractional derivative of the minus logarithmic function of 1 − x i (see for instance [30]), that is,…”

Section: Mathematical Resultsmentioning

confidence: 99%

Fractional-Order Susceptible-Infected Model: Definition and Applications to the Study of COVID-19 Main Protease

Abadías

Estrada-Rodriguez

Estrada

2020

Fract Calc Appl Anal

View full text Add to dashboard Cite

We propose a model for the transmission of perturbations across the amino acids of a protein represented as an interaction network. The dynamics consists of a Susceptible-Infected (SI) model based on the Caputo fractional-order derivative. We find an upper bound to the analytical solution of this model which represents the worse-case scenario on the propagation of perturbations across a protein residue network. This upper bound is expressed in terms of Mittag-Leffler functions of the adjacency matrix of the network of inter-amino acids interactions. We then apply this model to the analysis of the propagation of perturbations produced by inhibitors of the main protease of SARS CoV-2. We find that the perturbations produced by strong inhibitors of the protease are propagated far away from the binding site, confirming the long-range nature of intra-protein communication. On the contrary, the weakest inhibitors only transmit their perturbations across a close environment around the binding site. These findings may help to the design of drug candidates against this new coronavirus.

show abstract

“…Observe that the left-hand side of the above system is the Caputo fractional derivative of the minus logarithmic function of 1 − x i (see for instance [30]), that is,…”

Section: Mathematical Resultsmentioning

confidence: 99%

Fractional-Order Susceptible-Infected Model: Definition and Applications to the Study of COVID-19 Main Protease

Abadías

Estrada-Rodriguez

Estrada

2020

Fract Calc Appl Anal

View full text Add to dashboard Cite

show abstract

“…Among them, ( ) q  is a function introduced for the convenience of writing [7]. It appears in the second part of the integral 0 ( ) q q q qf dq  on the right side of the dy equation.…”

Section: The Parametric Equation and Practical Equation Of The Best T...mentioning

confidence: 99%

Fractional Differential Equations in Sports Training in Universities

Zhou

2022

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

The article theoretically analyzes the relevant knowledge of shot put in the shot put sports training of colleges and universities. The fractional differential equations are used to analyze the influence of the initial speed and the shot situation on the performance of the shot put. We obtain the joint angles of each stage of the shot throw through experimental design, time-consuming, final speed, limb displacement, shot-put shot speed, height, angle, and other kinematic parameters, and the shot-put motion trajectory of the picture stroke of the relevant action characteristics.

show abstract

“…e main objective is to illustrate the numerical scheme presented in previous Section 4. We set the 4 Complexity following values for the parameters of the model a � 1, b � 1, and c � 1 and the initial conditions given by equation (9). For Figure 1, the considered order is α � 0.95.…”

Section: Illustration Of the Numerical Schemementioning

confidence: 99%

“…Fractional calculus finds many recent advancements in fractional operators and their applicability in real-world problems. For recent advances of fractional calculus and its applications, see the following investigations [1,[6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Study of a Fractional‐Order Chaotic System Represented by the Caputo Operator

Sene

2021

Complexity

View full text Add to dashboard Cite

This paper is presented on the theory and applications of the fractional-order chaotic system described by the Caputo fractional derivative. Considering the new fractional model, it is important to establish the presence or absence of chaotic behaviors. The Lyapunov exponents in the fractional context will be our fundamental tool to arrive at our conclusions. The variations of the model’s parameters will generate chaotic behavior, in general, which will be established using the Lyapunov exponents and bifurcation diagrams. For the system’s phase portrait, we will present and apply an interesting fractional numerical discretization. For confirmation of the results provided in this paper, the circuit schematic is drawn and simulated. As it will be observed, the results obtained after the simulation of the numerical scheme and with the Multisim are in good agreement.

show abstract

Fractional derivative of logarithmic function and its applications as multipurpose ASP circuit

Cited by 7 publications

References 26 publications

Fractional-Order Susceptible-Infected Model: Definition and Applications to the Study of COVID-19 Main Protease

Fractional-Order Susceptible-Infected Model: Definition and Applications to the Study of COVID-19 Main Protease

Fractional Differential Equations in Sports Training in Universities

Study of a Fractional‐Order Chaotic System Represented by the Caputo Operator

Contact Info

Product

Resources

About