Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators

The human thermal comfort is the state of mind, which is affected not only by the physical and body’s internal physiological phenomena but also by the clothing properties such as thermal resistance of clothing, clothing insulation, clothing area factor, air insulation, and relative humidity. In this work, we extend the one-dimensional Pennes’ bioheat transfer equation by adding the protective clothing layer. The transient temperature profile with the clothing layer at the different time steps has been carried out using a fully implicit Finite Difference (FD) Scheme with interface condition between body and clothes. Numerically computed results are bound to agree that the clothing insulation and air insulation provide better comfort and keep the body at the thermal equilibrium position. The graphical representation of the results also verifies the effectiveness and utility of the proposed model.

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“…Future work should include extension of the model to higher dimensions and use of fractional derivatives as studied in [23][24][25].…”

Section: Discussionmentioning

confidence: 99%

Bioheat Transfer Equation with Protective Layer

Luitel

Gurung

Khanal

et al. 2021

Mathematical Problems in Engineering

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“…( 6) is a normalization function such that M(0) = M(1) =1. The Atangana-Baleanu fractional derivative (ABFD), in the Caputo sense, is [36][37][38]]…”

Section: Fractional Derivatives (Fds)mentioning

confidence: 99%

Analytic Solutions of Fractal and Fractional Time Derivative-Burgers–Nagumo Equation

Abdel‐Gawad

Tantawy

Abdel-Aziz

et al. 2021

Int. J. Appl. Comput. Math

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The Nagumo equation describes a reaction-diffusion system in biology. Here, it is coupled to Burgers equation, via including convection, which is the Burgers-Nagumo equation (BNE). The first objective of this work is to present a theorem to reduce, approximately, the different versions of the fractional time derivatives (FTD) to an ordinary derivative (OD) with time dependent coefficients (non autonomous). The second objective is to find the exact solutions of the fractal and FTD-BNE is reduced to BNE with time dependent coefficient. Further similarity transformations are introduced. The unified and extended unified method are used to find the exact traveling waves solutions. Also, self-similar solutions are obtained. The novelties in this work are (i) reducing, via an analytic approximation, the different versions of FTD to non autonomous OD. (ii) Traveling and self-similar waves solutions of the FTD-BNE are derived. (iii) The effect of the order of fractional and fractal derivatives, on waves structure, are investigated. It is found that significant fractal effects hold for smaller order derivatives. While significant fractional effects hold for higher-order derivatives. It is found that, the solutions obtained show solitary wave, wrinkle soliton, solitons with double kinks or with spikes and undulated wave. Further It is shown that wrinkle soliton, with double kink configuration holds for smaller fractal order. While in the case of fractional derivative, this holds for higher orders. We mention that the results found here are completely new. Symbolic computations are carried by using Mathematica.

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“…Although there are relations between these different types of fractional operators, they may differ in the physical interpretation of the definitions. For more information and application for fractional calculus, we refer the reader to other studies 3–24 . Therefore, in order to benefit from many advantages of the fractional‐order operator, especially the memory effect, we analyze the abovementioned phytoplankton growth and biological models theoretically and numerically with the help of Caputo fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Analysis of fractional‐order nonlinear dynamic systems under Caputo differential operator

Yusuf

Acay

2021

Math Methods in App Sciences

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The current study presents a detailed analysis of two crucial real‐world problems under the Caputo fractional derivative in order to deliver some desired results for the ecosystem. In view of the fact that memory effect plays a vital role in the application, we utilize an advantageous non‐local fractional operator to investigate and analyze a mathematical model of the planktonic ecosystem and biological system for the ecosystem on Planet GLIA‐2. On the other hand, theoretical and numerical results are given for the model created for phytoplankton, which is of great importance in preventing global warming, and the biological model. Existence and uniqueness are discussed for the solutions of both models with the help of the fixed‐point theorem under the Caputo operator. Additionally, the first‐order convergent numerical technique which is accurate, conditionally stable, and convergent in obtaining the solution of fractional‐order nonlinear systems of ordinary differential equations is utilized to simulate the two governing models. Numerical simulations including different values of arbitrary order ρ indicate the righteousness of the conditions for phytoplankton, Jancor, Murrot, and Vekton populations to develop.

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Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators

Cited by 34 publications

References 46 publications

Bioheat Transfer Equation with Protective Layer

Bioheat Transfer Equation with Protective Layer

Analytic Solutions of Fractal and Fractional Time Derivative-Burgers–Nagumo Equation

Analysis of fractional‐order nonlinear dynamic systems under Caputo differential operator

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