Numerical study of time-fractional fourth-order differential equations with variable coefficients

AbstractIn this article, we study numerical solutions of time-fractional fourth-order partial differential equations with variable coefficients by introducing the fractional derivative in the sense of Caputo. We implement reliable series solution techniques namely Adomian decomposition method (ADM) and He’s variational iteration method (HVIM). Some applications are presented to highlight the significant features of these techniques. The comparison shows that the solutions obtained are in good agreement with each other and with their respective exact solutions. Some of these types of differential equations arise practically in the theory of transverse vibrations

Numerical Solution of System of Fractional Differential Equations in Imprecise Environment

Fractional calculus and fuzzy calculus theory, mutually, are highly applicable for showing different aspects of dynamics appearing in science. This chapter provides comprehensive discussion of system of fractional differential models in imprecise environment. In addition, presenting a new vast area to investigate numerical solutions of fuzzy fractional differential equations, numerical results of proposed system are carried out by the Grünwald‐Letnikov\u27s fractional derivative. The stability along with truncation error of the Grünwald‐Letnikov’s fractional approach is also proved. Moreover, some numerical experiments are performed and effective remarks are concluded on the basis of efficient convergence of the approximated results towards the exact solutions and on the depictions of error bar plots

A preliminary investigation of maintenance contributions to commercial air transport accidents

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. Aircraft maintenance includes all the tasks needed to ensure an aircraft’s continuing airworthiness. Accidents that result from these maintenance activities can be used to assess safety. This research seeks to undertake a preliminary investigation of accidents that have maintenance contributions. An exploratory design was utilized, which commenced with a content analysis of the accidents with maintenance contributions (n = 35) in the official ICAO accident data set (N = 1277), followed by a quantitative ex-post facto study. Results showed that maintenance contributions are involved in 2.8 ± 0.9% of ICAO official accidents. Maintenance accidents were also found to be more likely to have one or more fatalities (20%), compared to all ICAO official accidents (14.7%). The number of accidents with maintenance contributions per year was also found to have reduced over the period of the study; this rate was statistically significantly greater than for all accidents (5%/year, relative to 2%/year). Results showed that aircraft between 10 and 20 years old were most commonly involved in accidents with maintenance contributions, while aircraft older than 18 years were more likely to result in a hull loss, and aircraft older than 34 years were more likely to result in a fatality

The role of leadership in aviation safety and aircraft airworthiness

Ensuring aircraft are technically safe to operate is the realm of airworthiness, literally worthy of being in the air. This is achieved not only with technological tools and techniques, or with just personnel and manpower, it is guided and supervised by managers and leaders. As such, the objective of this paper is to understand the role leadership plays in maintaining aviation safety and aircraft airworthiness. To this end, a case study of the Hawker Sidley Nimrod XV230 accident that occured on September 2, 2006 near Kandahar in Afghanistan, was utilized. The study concluded that leadership is a key aspect, specifically finding that leaders are responsible for articulating the organizations vision, strategic objective setting, and monitoring the achievement of those objectives. It was concluded that operational airworthiness is direct dependent on the leadership ability to provide direction, workplace culture, continued learning, and established risk management systems for safe and airworthy operations

Analytical and numerical results of fractional differential-difference equations

In this paper, we examine the fractional differential-difference equation (FDDE) by employing the proposed sensitivity approach (SA) and Adomian transformation method (ADTM). In SA the nonlinear differential-difference equation is converted to infinite linear equations which have a wide criterion to solve for the analytical solution. By ADTM, the FDDE is converted into ordinary differential-difference equation that can be solved. We test both the techniques through some test problems which are arising in nonlinear dynamical systems and found that ADTM is equivalently appropriate and simpler method to handle than SA

Off-Centered Stagnation Point Flow of a Couple Stress Fluid towards a Rotating Disk

An investigation has been made to study the off-centered stagnation flow of a couple stress fluid over a rotating disk. The model developed for the governing problem in the form of partial differential equations has been converted to ordinary differential equations with the use of suitable similarity transformation. The analytical approximation has been made with the most promising analytical approach, homotopy analysis method (HAM). The convergence region of the obtained solution is determined and plotted. The effects of couple stress and nondimensional parameters have been observed on the flows of couple stress fluid. Also comparison has been made with the Newtonian fluid as the special case of considered problem

On solutions of nonlinear time-space fractional Swift–Hohenberg equation: A comparative study

In this paper, a comparison for the solutions of nonlinear Swift–Hohenberg equation with time-space fractional derivatives has been analyzed. The two most promising techniques, fractional variational iteration method (FVIM) and the homotopy analysis method have been chosen for the comparison. The two different definitions of fractional calculus are considered to solve time-fractional derivative separately for the considered approaches. Also, the space fractional derivative is described in the Reisz sense. Analytical and numerical solutions for various combinations of the parameters are obtained. Numerical comparisons have been made for different values of parameters and depicted

Parameters Approach Applied on Nonlinear Oscillators

We applied an approach to obtain the natural frequency of the generalized Duffing oscillator u¨ + u + α3u3 + α5u5 + α7u7 + ⋯ + αnun=0 and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection u¨+αu|u|n−1=0. This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of n, the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain