New Results of Some of the Conformable Models Arising in Dynamical Systems

Abstract

This article investigates the new results of three nonlinear conformable models (NLCMs). To study such varieties of new soliton structures, we perform the generalized Kudryashov (GK) method. The obtained new results are defined in the styles of the exponential and rational functions. The derived new soliton structures are stable, serviceable, and fitting to embrace the conformable dynamics, chaotic vibrations, global bifurcations, optimal control problems, fluid mechanics, plasma physics, system identification, local bifurcations, control theory and resonances, and so many. The outcomes declare that the process is hugely valuable and accessible for investigating nonlinear conformable order models treated in theoretical physics.

Analyzing Soliton Solutions of the Extended (3 + 1)-Dimensional Sakovich Equation

“…where ψ(ξ) is exhibited by Equation (8). By substituting Equation ( 12) into Equation (11) and gathering all the same terms, these equations are transformed into polynomials of A(B 1 , B 2 , B 3 , B 4 ) = 0, α, β, γ and ω. Family 1: Setting…”

“…Hence, the discovery of analytical solutions for these equations is crucial in comprehending their dynamics and elucidating the underlying mechanisms governing their existing states. Diverse researchers have successfully employed, developed, and refined a range of innovative approaches to obtain exact solutions for NPDEs, such as the modified and extended rational expansion method [1], the G ′ /(bG ′ + G + a)-expansion technique [2], similarity transformations [3], the Hirota bilinear method [4], the homogenouous balance method [5], the tanh technique [6], Chupin Liu's theorem [7], the first integral technique [8], auto-Backlund transformations [9], the sine-Gordon equation method [10], the modified G ′ /G -expansion method [11], the Riccati equation mapping method [12], the new Kudryashov technique [13], conservation laws [14,15], the Jacobian elliptic function expansion technique [16], Riccati-Bernoulli's sub-ODE technique [17], the sec h p function method [18], Painlevé integrability [19], and so on.…”

Computational Analysis of Fractional-Order KdV Systems in the Sense of the Caputo Operator via a Novel Transform

“…FC more precisely and aggressively defines physical phenomena than classical calculus. Fractionalorder nonlinear models are widely used in many areas and are also important in nonlinear wave phenomena [3,4]. Fractional derivatives have been defined in several ways, including the Riemann-Liouville, Caputo, and Grunwald-Letnikov operators, the most well known of which are the Caputo and Riemann-Liouville fractional derivatives, which have often been employed in recent research.…”

Nonclassical Parametric Variational Technique to Manipulability Control of a Serial-Link Robot That Is Used in Treatment of Femoral Shaft Fractures

“…One significant class of these systems, known as DAC-SYS (differential-algebraic control systems), comprises systems controlled by mechanical differential algebra [5][6][7]. These systems find wide application in various fields, including robot dynamics, machine dynamics, and vehicle dynamics [8][9][10], with the principles of multibody system theory being employed in each case. When subsystems are coupled by constraints or when kinematic linkages such as joints are utilised, constraint equations can be explicitly incorporated, resulting in a mathematical model with differential-algebraic equations [11,12].…”