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,...
In applied research, fractional calculus plays an important role for comprehending a wide range of intricate physical phenomena. One of the Klein-Gordon model’s peculiar case yields the Phi-four equation. Additionally, throughout the past few decades it has been utilized to explain the kink and ...
One of the core concepts of contemporary control theory is the idea that a dynamical system can be controlled. Several abstract settings have been developed to describe the distributed control systems in a domain in which the control is acted through the boundary. In this manuscript, we investigat...
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...
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, ...
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 ...
It can be seen from equation (5) that adding the fractional-order derivative into the underdamped SR can make the current value of output x(t) highly depend on historical values of the past. Due to the above reason, the fractional-order derivative can enhance the weak signal detection of ...
At each fixed point, we calculate the eigenvalue of the satellite system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional-orders in the offered system. Additionally, the sample ...
2.1.1745 Part 1 Section 22.9.2.14, ST_TwipsMeasure (Measurement in Twentieths of a Point) 2.1.1746 Part 1 Section 22.9.2.16, ST_UnsignedDecimalNumber (Unsigned Decimal Number Value) 2.1.1747 Part 1 Section 22.9.2.19, ST_Xstring (Escaped String) 2.1.1748 Part 1 Section 23.2.1, sche...
{\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, ...