The Behavior of Logistic Equation with Alley Effect in Fuzzy Environment: Fuzzy Differential Equation Approach

Salahshour, Soheil; Ahmadian, Ali; Mahata, Animesh; Mondal, Sankar Prasad; Alam, Shariful

doi:10.1007/s40819-018-0496-8

Cited by 24 publications

(12 citation statements)

References 36 publications

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“…Proof: See paper [58] The parametric form of derivative of a fuzzy valued function is two types when the function is (i)-gH differentiable and (ii)-gH differentiable [59].…”

Section: Characterization Theorem For Differential Equation In Fuzzy Environmentmentioning

confidence: 99%

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Khaliq

Iqbal

Bhat

2021

Preprint

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Most of the cancer growth models have described the exponential growth patterns at the very initial stage with low cell population density. Eventually, decreasing the tumor growth rate at higher cell population densities because of deficiency in resources such as space and nutrients. However, recent studies at clinical and preclinical investigations of cancer initiation or reappaearance showed a population dynamics evincing that the growth rate increases as cell number increases. Hence, showing behaviour analogous to cooperative mechanism in the ecosystem and ecological effect called Allee effect. Based on these observations with two arguments i.e. change in initial population and growth rate. In this paper, the novel mathematical model of tumor growth kinetics with Allee effect under fuzzy environment is proposed. In this model the Generalized Hukuhara derivative approach is utilized to solve the fuzzy differential equations. Moreover, it is showen that the change in initial value and growth rate affects the cell density with the Allee effect under the fuzzy environment. Finally the superiority of model has been showen with the help of numerical simulation.

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“…Proof: See paper [58] The parametric form of derivative of a fuzzy valued function is two types when the function is (i)-gH differentiable and (ii)-gH differentiable [59].…”

Section: Characterization Theorem For Differential Equation In Fuzzy Environmentmentioning

confidence: 99%

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Khaliq

Iqbal

Bhat

2021

Preprint

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“…Gasilov et al [27] studied the system of FDEs with the help of TFNs. Salahsour et al [28] studied the fuzzy logistic equation and alley effect using FDEs with the help of TFNs. e fuzzy boundary value problems (FBVPs) depend on the concept of the solution of FDE.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of MHD Third-Grade Fluid Flow through an Inclined Channel with Ohmic Heating under Fuzzy Environment

Nadeem

Siddique

Jarad

et al. 2021

Mathematical Problems in Engineering

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The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette–Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of α -cut approach, which controls the fuzzy uncertainty. It is observed that the fuzzy gravitational and magnetic parameters are less sensitive for a better flow and heat situation. Using triangular fuzzy numbers (TFNs), the left, right, and mid values of the velocity and temperature profile are presented due to various values of the involved parameters in tabular form. For validation, the present results are compared with existing results for some special cases, viz., crisp case, and they are found to be in good agreement.

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“…Gasilov et al [ 51 ] studied the system of FDEs with the TFNs. Salahshour et al [ 52 ] studied the fuzzy logistic equation and alley effect using FDEs with the help of TFNs. Biswal et al [ 53 ] studied the natural convection of nanofluid flow between two parallel plates using the HPM in a fuzzy environment.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of MHD Couette Flow of a Fuzzy Nanofluid through an Inclined Channel with Thermal Radiation Effect

Siddique

Zulqarnain

Nadeem

et al. 2021

Computational Intelligence and Neuroscience

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The present study especially concerns the investigation of the Couette flow and heat transfer with thermal radiation through an inclined channel. Single-wall carbon nanotube (SWCNT) and multiple-wall carbon nanotube (MWCNT) are nanoparticles embedded in the host fluid. The dimensionless highly nonlinear differential equations (DEs) are solved via numerical scheme bvp4c. The effects of the physical parameters on heat transfer are presented in the form of graphs. The results demonstrate that the heat transfer is enhanced by using solid particle frictions (SWCNT and MWCNT). The large estimation of a magnetic parameter declines the velocity component. The current and existing results with their comparisons are shown in the tabular form for the validation of our code. The current results are in good agreement with their existing results. Generally, fuzziness or uncertainty is inherent in modeling, analysis, and experimentation. Due to the uncertain environmental conditions, fuzziness broadly exists in various engineering heat transfer problems. In this work, the nanoparticles’ volume fraction of the SWCNT and MWCNT is taken as uncertain parameters in terms of triangular fuzzy numbers (TFNs). The TFNs are controlled by the α − cut which has less computational effort for analyzing the fuzziness or uncertainties. Also, a comparison between the SWCNT and MWCNT through the membership function and the variability of the uncertainty is studied.

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The Behavior of Logistic Equation with Alley Effect in Fuzzy Environment: Fuzzy Differential Equation Approach

Cited by 24 publications

References 36 publications

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Numerical Study of MHD Third-Grade Fluid Flow through an Inclined Channel with Ohmic Heating under Fuzzy Environment

Numerical Simulation of MHD Couette Flow of a Fuzzy Nanofluid through an Inclined Channel with Thermal Radiation Effect

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