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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 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.
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%.
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In the matter of deliberate design, well-studied histories of artifact systems through time repeatedly show innovations that are not the simple, linear modifications of earlier, preexisting structures.
Our results are compared to results by Böröczky Schneider and Artstein Milman, who showed that in many cases, the property of order reversing is sufficient to determine a duality operation, up to obvious linear modifications.
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}).
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 Osher Chakrabarthy family of linear flux-modification schemes is considered.
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