Note By applying the series of \(\zeta _m(\aleph )\) from Eq. (11) into Eq. (4), it is possible to obtain the power series of \(\mathfrak {S}(\aleph , \wp )\) in multiple fractional form at the value of \(\wp =\wp _0\) as follows,...
1 Properties of solitons. a. Linear energy bands (grey) for the model described in the main text at Ωz/2π=0.3 together with the nonlinear eigenvalue of a soliton (red) for increasing nonlinearity. Dashed line marks a nonlinear bifurcation point, with a corresponding slope change. b. ...
In this paper, we investigate the presence of positive solutions for system of fractional q-differential inclusions involving sequential derivatives with respect to the p-Laplacian operator. By using fixed point technique we obtain a new solution for inclusion or boundary value problems with special in...
With respect to Regiomontanus's perception of the value of the base circle radius, just prior to the two Sine tables in the Compositio tabularum he states: Thus you have found the sine, with the [sinus] totus [R, radius of base circle] 6000000; and if you wish to have the same [si...
The solution to this problem typically involves the use of fractional polynomials types, i.e. Chebyshev and Bassel polynomials. Keywords: fractional order optimal control problem; two-point boundary value problem; fractional order differential equation; fractional delay differential equation; numerical ...
The value of μ-sensitivity with respect to a particular system parameter, is an indication of how critical is that parameter from stability point of view. The method of μ-sensitivity is applied to a PI controlled dc/dc buck converter system with input LC filter in [33], wherein μ-...
By choosing a fractional value of l, the beam source, whose electric field is given by Eq. (1), is termed a fractional vortex beam. Various fractional vortex beams have been proposed by varying the amplitude and phase term, including fractional Gaussian vortex beams, fractional BG beams, ...
We introduce the investigation of approximate controllability for a new class of nonlocal and noninstantaneous impulsive Hilfer fractional neutral stochastic integrodifferential equations with fractional Brownian motion. An appropriate set of sufficient
In addition, ϖϖ indicates the value of the fraction-order that is normally selected in range ϖ ∈ (0,1)ϖ ∈ (0,1). Theorem 2.11 The semi-group property of the fractional-order differential can be described as: If f(t) ∈ C[0,κ]f(t) ∈ C[0,κ], κ>0κ>0, α...
{\omega }_{0}|/\gamma )whereGis a log-periodic function,βandγare scaling constants that depend on the choice of the central frequency51. In addition, both therj(ω) and the product of thetj(ω) are self-similar functions, as illustrated in Fig. (6). For a fixed value ofω, ...