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Fish farming, a potential activity for the production of protein with high nutritional value, has emerged as a substantial source of income in the modern world. The degradation of natural materials uses oxygen to reduce them below the life-support stage. A huge area with an excessive amount of water swamp for oxygen exchange makes for the ideal ecosphere for fish farming, yet the mussel population may grow swiftly in a really modest water swapping farm producing a lot of feed. In this study, we examine the dynamics and chaotic behavior of a fish farm model containing populations of nutrients and mussels with different kernels insight of fractal-fractional operator. We examined the positively invariant area as well as demonstrate positive, bounded solutions of the model. We also show the equilibrium states for the occurrence and extinction of species. We prove the existence and uniqueness of positive solutions through fixed-point theorems and verified the Ulam–Hyers stability for proposed model. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version for the various kernels, which include the power-law and Mittag–Leffler kernel. We develop some numerical simulations to test our theoretical conclusions with chaotic behavior at different fractional-order values.

In this paper, an efficient numerical model applicable for wide varieties of long channel field-effect transistors (MOSFET, MESFET, HEMT, etc.) is developed. A set of available data is used to calculate the model parameters and another set of data is used to verify the accuracy of the model. This model provides a single expression that is applicable for the entire range of device biasing and can predict the output parameters with less than 1% error compared to the experimental results. Lagrange polynomial, the highest degree of polynomial for any given set of data, is used to derive the model from available data. This method is efficient in the sense that it can be derived from a limited number of experimental data and since it uses only one equation for entire range of the device operation hence its computational cost is also small.

In this paper, we present the Lagrange polynomial solutions to system of higher-order linear integro-differential Volterra–Fredholm equations (IDVFE). This method transforms the IDVFE into the matrix equations which is converted to a system of linear algebraic equations. Some numerical results are given to illustrate the efficiency of the method.

In this paper, an efficient numerical model applicable for wide varieties of long channel field-effect transistors (MOSFET, MESFET, HEMT, etc.) is developed. A set of available data is used to calculate the model parameters and another set of data is used to verify the accuracy of the model. This model provides a single expression that is applicable for the entire range of device biasing and can predict the output parameters with less than 1% error compared to the experimental results. Lagrange polynomial, the highest degree of polynomial for any given set of data, is used to derive the model from available data. This method is efficient in the sense that it can be derived from a limited number of experimental data and since it uses only one equation for entire range of the device operation hence its computational cost is also small.

In the paper a novel method for determination of the time behavior trend line of a 1 Ω resistance standard by using the stochastic genetic algorithm is given. For modeling of the trend line a Lagrange polynomial (LP) is acquired. The coefficients of the LP are determined from the experimental data from previous calibrations of the resistance standard. The goal function of the optimization process by genetic algorithm is the minimum difference between the theoretical resistance value, derived by the LP, and the experimental value of the resistance at certain time moment. The uncertainties of the experimental data are the mapping range of the input data during the stochastic evolution of the LP trend line. A verification of the gained model with known experimental data is done.