Mathematical modeling of anisotropic visco-elastic environments with memory based on integro-differentiation of fractional order

2018 ◽  
Author(s):  
Sokolovskyy Yaroslav ◽  
Levkovych Maryana ◽  
Mokrytska Olha ◽  
Atamanyuk Vitalij
Keyword(s):  
Mathematical Modeling ◽  
Fractional Order ◽  
With Memory

scholarly journals Analysis and Dynamics of Fractional Order Covid-19 Model with Memory Effect

2021 ◽  
pp. 104017
Author(s):  
Supriya Yadav ◽  
Devendra Kumar ◽  
Jagdev Singh ◽  
Dumitru Baleanu
Keyword(s):  
Memory Effect ◽  
Fractional Order ◽  
With Memory

scholarly journals Exponential Attractors for the 3D Fractional-order Bardina Turbulence Model With Memory and Horizontal Filtering

2021 ◽  
Author(s):  
Michele Annese ◽  
Luca Bisconti ◽  
Davide Catania
Keyword(s):  
Phase Space ◽  
Fractional Order ◽  
Turbulence Model ◽  
Memory Term ◽  
Exponential Attractor ◽  
Exponential Attractors ◽  
Regularity Properties ◽  
Hereditary Effects ◽  
With Memory ◽  
Simplified Bardina

AbstractWe consider the 3D simplified Bardina turbulence model with horizontal filtering, fractional dissipation, and the presence of a memory term incorporating hereditary effects. We analyze the regularity properties and the dissipative nature of the considered system and, in our main result, we show the existence of a global exponential attractor in a suitable phase space.

scholarly journals The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 987 ◽  
Author(s):  
A. A. Alderremy ◽  
Hassan Khan ◽  
Rasool Shah ◽  
Shaban Aly ◽  
Dumitru Baleanu
Keyword(s):  
Mathematical Modeling ◽  
Analytical Solution ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Analytical Techniques ◽  
Whitham Equations ◽  
Suggested Technique ◽  
Approximate Analytical Solutions ◽  
Physical Phenomena

This article is dealing with the analytical solution of Fornberg–Whitham equations in fractional view of Caputo operator. The effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems. The approximate analytical solutions of nonlinear numerical problems are determined to confirm the validity of the suggested technique. The solution of the fractional-order problems are investigated for the suggested mathematical models. The solutions-graphs are then plotted to understand the effectiveness of fractional-order mathematical modeling over integer-order modeling. It is observed that the derived solutions have a closed resemblance with the actual solutions. Moreover, using fractional-order modeling various dynamics can be analyzed which can provide sophisticated information about physical phenomena. The simple and straight-forward procedure of the suggested technique is the preferable point and thus can be used to solve other nonlinear fractional problems.

scholarly journals Numerical behavior of a fractional order dynamical model of RNA silencing

2016 ◽  
Vol 4 (2) ◽  
pp. 52
Author(s):  
A.M.A. El-Sayed ◽  
M. Khalil ◽  
A.A.M. Arafa ◽  
Amaal Sayed
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Detailed Analysis ◽  
Fractional Order ◽  
Rna Silencing ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
The Stability ◽  
Predictor Corrector ◽  
With Memory

A class of fractional-order differential models of RNA silencing with memory is presented in this paper. We also carry out a detailed analysis on the stability of equilibrium and we show that the model established in this paper possesses non-negative solutions. Numerical solutions are obtained using a predictor-corrector method to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. Numerical simulations are presented to illustrate the results. Also, the numerical simulations show that, modeling the phenomena of RNA silencing by fractional ordinary differential equations (FODE) has more advantages than classical integer-order modeling.

scholarly journals Dynamic Hedging Based on Fractional Order Stochastic Model with Memory Effect

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Qing Li ◽  
Yanli Zhou ◽  
Xinquan Zhao ◽  
Xiangyu Ge
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Fractional Order ◽  
Minimum Variance ◽  
Hedge Ratio ◽  
Out Of Sample ◽  
Sample Test ◽  
Optimal Dynamic ◽  
Optimal Hedge ◽  
With Memory

Many researchers have established various hedge models to get the optimal hedge ratio. However, most of the hedge models only discuss the discrete-time processes. In this paper, we construct the minimum variance model for the estimation of the optimal hedge ratio based on the stochastic differential equation. At the same time, also by considering memory effects, we establish the continuous-time hedge model with memory based on the fractional order stochastic differential equation driven by a fractional Brownian motion to estimate the optimal dynamic hedge ratio. In addition, we carry on the empirical analysis to examine the effectiveness of our proposed hedge models from both in-sample test and out-of-sample test.

scholarly journals Fractional order mathematical modeling of COVID-19 transmission

2020 ◽  
Vol 139 ◽  
pp. 110256 ◽  
Author(s):  
Shabir Ahmad ◽  
Aman Ullah ◽  
Qasem M. Al-Mdallal ◽  
Hasib Khan ◽  
Kamal Shah ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Fractional Order

Optimal Control of a Fractional-Order HIV-Immune System With Memory

2012 ◽  
Vol 20 (3) ◽  
pp. 763-769 ◽  
Author(s):  
Yongsheng Ding ◽  
Zidong Wang ◽  
Haiping Ye
Keyword(s):  
Optimal Control ◽  
Immune System ◽  
Fractional Order ◽  
With Memory

Determination of the fractional order in semilinear subdiffusion equations

2020 ◽  
Vol 23 (3) ◽  
pp. 694-722
Author(s):  
Mykola Krasnoschok ◽  
Sergei Pereverzyev ◽  
Sergii V. Siryk ◽  
Nataliya Vasylyeva
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Computational Algorithm ◽  
Optimality Criterion ◽  
Small Time ◽  
Inverse Boundary ◽  
Regularization Scheme ◽  
Numerical Tests ◽  
With Memory

AbstractWe analyze the inverse boundary value-problem to determine the fractional order ν of nonautonomous semilinear subdiffusion equations with memory terms from observations of their solutions during small time. We obtain an explicit formula reconstructing the order. Based on the Tikhonov regularization scheme and the quasi-optimality criterion, we construct the computational algorithm to find the order ν from noisy discrete measurements. We present several numerical tests illustrating the algorithm in action.

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