A comparative study of convective fluid motion in rotating cavity via Atangana–Baleanu and Caputo–Fabrizio fractal–fractional differentiations

Abro, Kashif Ali; Atangana, Abdon

doi:10.1140/epjp/s13360-020-00136-x

Cited by 109 publications

(25 citation statements)

References 36 publications

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“…Many researchers studied a large number of fractional-order aspects of the biological process (see [9][10][11][12][13]). Those aspects should not be shown and explained by the integer-order calculus, but the fractional calculus can do it.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Kaviya

Muthukumar

2021

Eur. Phys. J. Plus

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Aim of this work is to study the four species various fractional-order prey-predator or Lotka-Volterra (LV) system with both immigration and harvesting effects. The existence and uniqueness, uniform boundedness, persistence, permanence, and extinction of this system solution are analyzed. The stability behavior of the system is obtained with the help of the Routh-Hurwitz (RH) stability criterion. The small changes in fractional-order values can produce a significant impact on the stability of the system is confirmed. This work verifies that the small amount of immigration effect can change the dynamic nature of the LV system. Numerical results are given to illustrate the obtained theoretical results of the stability analysis. The bionomic equilibrium points of the system are attained with their feasibility conditions. To get the optimal amount of harvesting effect with the Pontryagin's maximum principle, the harvesting parameter is considered as the control parameter.

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Section: Introductionmentioning

confidence: 99%

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Kaviya

Muthukumar

2021

Eur. Phys. J. Plus

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“…As compared to classical models, the memory effect is much stronger in fractional derivatives. The non‐integer differential operators lie in the field of fractional calculus through which several different possibilities for defining complex number or real number powers of the differentiation and integration operators are valid 19‐22 . Mocherla et al 23 investigated the melting heat transfer for the Maxwell fluid flow through a stretching sheet by invoking the suitable similarity transmutations subject to the sake of regular profiles (velocity, concentration, and temperature).…”

Section: Introductionmentioning

confidence: 99%

Role of single slip assumption on the viscoelastic liquid subject to non‐integer differentiable operators

Saeed

Abro

Almani

2021

Math Methods in App Sciences

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The main focus of this study is to investigate the impact of heat generation/absorption with single slip assumptions based on Newtonian heating on magnetohydrodynamic (MHD) time‐dependent Maxwell fluid over an unbounded plate embedded in a permeable medium. The mathematical modeling based on fractional treatment of governing equation subject to the temperature distribution, shearing stress, and velocity field is developed. The fractionalized analytical solutions have been traced out separately through Atangana‐Baleanu (AB) and Caputo‐Fabrizio (CF) fractional differential operators. These differential operators with and without non‐locality have been employed on the developed governing partial differential equations. The mathematical analysis of developed fractionalized governing partial differential equations has been established by means of systematic and powerful techniques of Laplace transform with its inversion. For the sake of physical investigation of the considered problem, the effective Prandtl number and fractional parameter have been invoked on temperature with and without single slip assumption. Our results suggest that the velocity profile decrease by increasing the effective Prandtl number. The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. Additionally, the magnetic field and relaxation phenomenon have been analyzed on the profile of velocity with and without single slip assumption.

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“…They claimed that new strange behaviors of the attractors were not possible by only classical differentiations. In short, the study can be continued for the charming and effective role of fractional calculus in applied engineering problems, 20–31 but we include here recent attempt in categorically as epidemiology, 32–39 heat and mass transfer, 40–44 fluid mechanics, 45–47 nanofluids, 48–51 and electrical engineering 52–55 . Motivating by above discussion, our aim is to propose the controlling analysis and coexisting attractors provided by memristor through highly nonlinear for mathematical relationships of governing differential equations.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study

Abro

Atangana

2020

Math Methods in App Sciences

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The newly generalized energy storage component, namely, memristor, which is a fundamental circuit element so called universal charge‐controlled mem‐element, is proposed for controlling the analysis and coexisting attractors. The governing differential equations of memristor are highly nonlinear for mathematical relationships. The mathematical model of memristor is established in terms of newly defined fractal‐fractional differential operators so called Atangana‐Baleanu, Caputo‐Fabrizio, and Caputo fractal‐fractional differential operator. A novel numerical approach is developed for the governing differential equations of memristor on the basis of Atangana‐Baleanu, Caputo‐Fabrizio, and Caputo fractal‐fractional differential operator. We discussed chaotic behavior of memristor under three criteria such as (i) varying fractal order, we fixed fractional order; (ii) varying fractional order, we fixed fractal order; and (ii) varying fractal and fractional orders simultaneously. Our investigated graphical illustrations and simulated results via MATLAB for the chaotic behaviors of memristor suggest that newly presented Atangana‐Baleanu, Caputo‐Fabrizio, and Caputo fractal‐fractional differential operators generate significant results as compared with classical approach.

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A comparative study of convective fluid motion in rotating cavity via Atangana–Baleanu and Caputo–Fabrizio fractal–fractional differentiations

Cited by 109 publications

References 36 publications

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Role of single slip assumption on the viscoelastic liquid subject to non‐integer differentiable operators

Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study

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