In this paper, we apply Picard operator theory to investigate a class of fractional differential equations with iterations of linear modification of the argument.
The importance of iterations of linear modification of the argument will help us to find a simple way and suitable parameter to find the solution.
Furthermore, in graded-index optical superlattices, the index gradient comes from a linear modification in the refractive indices of the layers [7, 8], and so on.
In [9], the author discussed a first-order differential equation with iterations of linear modification of the argument { x ′ ( t ) = f ( t, x ( t ), x ( λ t ), x ( λ x ( λ t ) ) ), 0 < λ < 1, t ∈ J b : = [ 0, b ], b > 0, x ( 0 ) = 0. (1).
This range of BWC gave rise to a linear modification of the assessed NIRS parameters with a maximum change of 10%.
These waves are propagating in a collisional, weakly magnetized ionosphere, and it has been argued that as such they should be damped through collisions, and the wave should not retain the characteristics of the whistler-mode because of non-linear modifications to the dispersion relation.
The modes include a non-linear modification to the linear, harmonic component as well as a static offset term and second and third harmonic components.
Within the problem of the authority estimation, we have used the non-linear modification of the polynomial function in the form (y = b_{0} + b_{1}x^{c_{1}} + {cdots } + b_{n}x^{cn}).
Finally, the interest of the methodology is illustrated by some practical problems in gear dynamics: i.e., the influence of some geometrical errors and the role of linear profile modifications on spur and helical gears.
