Fractional-Order Logistic Differential Equation with Mittag–Leffler-Type Kernel

In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations of each solution in terms of a formal power series. Some numerical approximations are implemented by using truncated series.

Galarkin Method with GeoGebra in Differential Equations

Let us consider d 2 y d x 2 + y = Q ( x , a ) , y ( 0 ) = y ( 1 ) = 0 , x , a ∈ ( 0 , 1 ) . . In the following paper, various differential equations will be displayed, which willbe solved using Galerkin’s numericla method and where formal solutions and their numerical approximations can be seen with GeoGebra animated Apptles.

On Weighted Simpson’s 38 Rule

Numerical approximations of definite integrals and related error estimations can be made using Simpson’s rules (inequalities). There are two well-known rules: Simpson’s 13 rule or Simpson’s quadrature formula and Simpson’s 38 rule or Simpson’s second formula. The aim of the present paper is to extend several inequalities that hold for Simpson’s 13 rule to Simpson’s 38 rule. More precisely, we prove a weighted version of Simpson’s second type inequality and some Simpson’s second type inequalities for Lipschitzian, bounded variations, convex functions and the functions that belong to Lq. Some applications of the second type Simpson’s inequalities relate to approximations of special means and Simpson’s 38 formula, and moments of random variables are made.