Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods

Effect of Space Fractional Parameter on Nonlinear Ion Acoustic Shock Wave Excitation in an Unmagnetized Relativistic Plasma

“…It is now fast-growing attention to the research community that fractional calculus has its huge applicability to study complex physical behavior in a diverse field of science and engineering. In another point of view, not only the model involving fractional-order derivatives (FDs) but also FO NLEEs abstracted from many physical problems [28][29][30][31] are applicable with the presence of any situations that arise in many branches of modern physics. The FO NLEEs, when compared to the integer order NLEEs, can more accurately explain the dynamic response of the actual system, boost dynamic system performance, and solve practical difficulties.…”

Dynamical plane wave solutions for the Heisenberg model of ferromagnetic spin chains with beta derivative evolution and obliqueness

“…It is noted that represents the normalized complex amplitude of the wave profile. Many research scholars [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] have devoted significant effort to revealing various types of traveling wave solutions for mathematical physics equations like Eq. (1) by considering many environments via several types of theoretical and computational architectures.…”

“…To overcome such difficulties, researchers have concentrated their efforts on fractional derivatives (FDs), such as conformable, Caputo, Riemann-Liouville derivatives, etc., in lieu of classical derivatives. Such FDs have been introduced in many mathematical physics equations [20] , [31] , [32] , [34] , [35] , [36] , [37] , [38] , [39] to understand the complex physical issues in the physical system. Very recently, the newly included FD, so called the Beta derivative (BD), has been proposed by Atangana et al [37] , which fulfills all the fundamental features of calculus and overcomes some limitations of the aforementioned FDs.…”

Lump and Interaction Solutions to the ( 3 + 1 )-Dimensional Variable-Coefficient Nonlinear Wave Equation with Multidimensional Binary Bell Polynomials

“…During the last years, the various analytical methods were developed to find the exact solutions by powerful scholars for interesting fields of research because of their wide number of applications in the engineering and manufacturing fields, nonlinear models, for example, nonlinear Schrodinger equation [36], the conformable nonlinear differential equation governing wave-propagation in low-pass electrical transmission lines [37], the (2 + 1)-dimensional coupled variant Boussinesq equations [38], the nonlinear directional couplers with metamaterials by including spatial-temporal fractional beta derivative evolution [39], a new (3 + 1)-dimensional Hirota bilinear equation [40], oblique resonant nonlinear waves with dual-power law nonlinearity [41], the coupled Schrödinger-Boussinesq system with the beta derivative [42], and the Hirota-Maccari system [43].…”