Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative

Abstract

In this paper, DSEK model with fractional derivatives of the Atangana-Baleanu Caputo (ABC) is proposed. This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DSEK model. According to this theory, we will define two operators based on Lipschitzian and prove that they are contraction mapping and relatively compact. Ulam-Hyers stability theorem is implemented to prove the fractional DSEK model’s stability in Banach space. Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α ∈ 0,1 and different step sizes h . Result discussion will be given, describing the changes that occur due to the step size h .

Freelance Model with Atangana–Baleanu Caputo Fractional Derivative

“…We use definitions in Equations ( 4)-( 6) for our calculations. For relations and properties of this derivative, readers can see [28]…”

“…Ref. [28] was the first to define the freelance model, where N represents the population that are working but not as a freelancer. F represents the freelancer population and I represents the information spread about freelancers, whether positive or negative.…”

“…be defined on the interval [0, w). Let v be the sub intervals of equal width be h = w v by using nodes t i = ih for i = 0, 1, • • • , v. The iterative equation in [28] is given as…”

“…For solving this model numerically, we consider the same parameters and initial values as given in [9]. According to [28], the parameters have value γ = 10, = 0.0002, δ = 0.02, µ = 0.03, a = 0.05, and b = 0.06. Now, the fractional freelance model in Equation ( 9) with the iterative formula, Equation (20) becomes…”

Hybrid Methodology for the Computational Behaviour of Thermal Radiation and Chemical Reaction on Viscoelastic Nanofluid Flow

“…Alharbi et al [37] explored the flow of hybrid nanofluid subjected to single-walled and multiwalled carbon nanotubes with the structures of the Brinkman-type fluid model. Khan et al [38] were concerned with the Atangana-Baleanu Caputo fractional derivative and its characteristics. A fixed-point scheme has been used to find the uniqueness and existence of solutions for the fractional DSEK model.…”