Purpose This study aims that very lately, Mohand transform is introduced to solve the ordinary and partial differential equations (PDEs). In this paper, the authors modify this transformation and associate it with a further analytical method called homotopy perturbation method (HPM) for the fractional view of Newell–Whitehead–Segel equation (NWSE). As Mohand transform is restricted to linear obstacles only, as a consequence, HPM is used to crack the nonlinear terms arising in the illustrated problems. The fractional derivatives are taken into the Caputo sense. Design/methodology/approach The specific objective of this study is to examine the problem which performs an efficient role in the form of stripe orders of two dimensional systems. The authors achieve the multiple behaviors and properties of fractional NWSE with different positive integers. Findings The main finding of this paper is to analyze the fractional view of NWSE. The obtain results perform very good in agreement with exact solution. The authors show that this strategy is absolutely very easy and smooth and have no assumption for the constriction of this approach. Research limitations/implications This paper invokes these two main inspirations: first, Mohand transform is associated with HPM, secondly, fractional view of NWSE with different positive integers. Practical implications In this paper, the graph of approximate solution has the excellent promise with the graphs of exact solutions. Social implications This paper presents valuable technique for handling the fractional PDEs without involving any restrictions or hypothesis. Originality/value The authors discuss the fractional view of NWSE by a Mohand transform. The work of the present paper is original and advanced. Significantly, to the best of the authors’ knowledge, no such work has yet been published in the literature.
No abstract is provided for this article.
Sevimlican suggested an effective algorithm for space and time fractional telegraph equations by the variational iteration method. This paper shows that algorithm can be updated by either variational iteration algorithm‐II or the fractional variational iteration method.
In this paper, we couple the iteration method with the perturbation method to solve the well-known Blasius equation. The obtained approximate analytic solutions are valid for the whole solution domain. Comparison with Howarth’s numerical solution reveals that the proposed method is of high accuracy, the first iteration step leads to 6.8% accuracy, and the second iteration step yields the 0.73% accuracy of initial slop.
An allometric scaling law between the metabolic rate of the total barks of a plant and its total bark mass is proposed, the scaling exponent is proved to be 2/3 for mature plants.
The lack of ultrasensitive biosensors is the major challenge in the control of pandemics at the very initial stage, so it is necessary to develop new biosensors for the prompt treatment, and the piezoelectric biosensor based on ultrasensitive MEMS system offers a good opportunity. This paper presents a novel approach using polyvinylidene fluoride (PVDF) unsmooth nanofibers to transfer electronic current. The unique unsmooth surface of these nanofibers provides a high surface energy (geometrical potential), making them highly sensitive to microorganisms (e.g., viruses) absorbed on their surface. The absorption of viruses has an obvious effect on the nanofiber’s displacement and electrical resistivity. This paper presents a mathematical model that demonstrates the system's ultra-sensitivity. This rigorous mathematical analysis shows that even when the pull-in voltage in the PVDF nanofiber changes by just 0.0589 %, a dramatic shift from normal periodic motion to pull-in motion is predicted. This paper provides a new and reliable theoretical way to detect pandemics at the very beginning stage.
When Newton found his interpolation formula in 1670, ancient Chinese mathematicians had used the formula in more sophisticated forms for more than one millennium. A new proof to those formulas are geometrically illustrated.
It is the most effective way to study the effect of global warming on plant morphology by analyzing a plant species on a mount along altitudinal gradients. Altitudinal increase means decrease of temperature and metabolic rate as well. This might affect the leaf morphology greatly. The SEM study reveals that the size of nanopore on the epidermis changes gradually along altitudinal gradients, and the absorbed fine particles on the leaf have almost same size, exhibiting high selectivity over other particles. The study gives a strong proof that morphology change links to global warming.
No abstract is provided for this article.
Pull-in instability was an important phenomenon in microelectromechanical systems (MEMS). In the past, MEMS were usually assumed to work in an ideal environment. But in the real circumstances, MEMS often work in dust-filled air, which is equivalent to working in porous media, that's mean fractal space. In this paper, we studied MEMS in fractal space and established the corresponding model. At the same time, we can control the occurrence time and stable time of pull-in by adjusting the value of the fractal index, and obtain a stable pull-in phenomenon.
The heat equation is re-studied in this Letter in view of variational theory. By the semi-inverse method, a variational principle for the heat conduction is obtained, which is first appeared in the literature. The physical understanding of the obtained variational principle still needs further explanation.
A generalized variational principle of 2D unsteady compressible flow around oscillating airfoils is established directly from the governing equations and boundary/initial conditions via the semi‐inverse method proposed by He. In this method, an energy integral with an unknown F is used as a trial‐functional. The identification of the unknown F is similar to the identification of the Lagrange multiplier. Based on the variational theory with variable domain, a variational principle for the inverse problem (given as the time‐averaged pressure over the airfoil contour, while the corresponding airfoil shape is unknown) is constructed, and all the boundary/initial conditions are converted into natural ones, leading to well‐posedness and the unique solution of the inverse problems.
Milk is mixed with polyvinyl alcohol solution with water as solvent, and the mixed solution is used for fabrication of polyvinyl alcohol-milk nanofibers by the electrospinning.
A fractional Adomian decomposition method for fractional nonlinear differential equations is proposed. The iteration procedure is based on Jumarie's fractional derivative. An example is given to elucidate the solution procedure, and the results are compared with the exact solution, revealing high accuracy and efficiency.
Purpose The purpose of this paper is to study the dynamical properties of a rotating rigid body (RB) containing a viscous incompressible fluid. Design/methodology/approach The Reynolds number is assumed to be small so that the governing equations can be easily obtained, and the asymptotic technique is used to solve the problem. Findings The effects of the various body parameter values on the motion’s behavior are theoretically elucidated, which can be used for optimization of the charged RB. Originality/value This paper finds the missing piece of the puzzle when it comes to the rotating RB containing a viscous fluid; it clearly elucidates graphically how the body parameters affect its dynamical properties.
In this paper, a new iteration method is proposed to solve nonlinear problems. Special attention is paid to nonlinear differential equations with convolution product nonlinearities. The results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems. Furthermore, the first order of approximations are more accurate than perturbation solutions at high order of approximation.
Every shallow-water wave propagates along a fractal boundary, and its mathematical model cannot be precisely represented by integer dimensions. In this study, we investigate a coupled fractal–fractional KdV system moving along an irregular boundary within the framework of variational theory, which is commonly employed to derive governing equations. However, not every fractal–fractional differential equation can be formulated using variational principles. The semi-inverse method proves to be challenging in finding an appropriate variational principle for nonlinear problems and eliminating extraneous components from the studied model. We consider the coupled fractal–fractional KdV system with arbitrary coefficients and establish its variational formulation to unveil the remarkable insights into the energy structure of the model and interrelationships among coefficients. Encouraging results are obtained for this coupled KdV system.
A new special function is introduced, and a variational formulation is established for two-dimensional incompressible inviscid flow, which might find potential applications in numerical simulation and various inverse problems.
