261 research outputs found
Shifted genocchi polynomials operational matrix for solving fractional order stiff system
In this paper, we solve the fractional order stiff system using shifted Genocchi poly�nomials operational matrix. Different than the well known Genocchi polynomials, we shift the
interval from [0, 1] to [1, 2] and name it as shifted Genocchi polynomials. Using the nice prop�erties of shifted Genocchi polynomials which inherit from classical Genocchi polynomials, the
shifted Genocchi polynomials operational matrix of fractional derivative will be derived. Collo�cation scheme are used together with the operational matrix to solve some fractional order stiff
system. From the numerical examples, it is obvious that only few terms of shifted Genocchi
polynomials is sufficient to obtain result in high accurac
Differential equation and complex network approaches for epidemic modelling
This study consists of three parts. The first part focuses on bifurcation analysis of epidemic models with sub-optimal immunity and saturated treatment/recovery rate as well as nonlinear incidence rate. The second part of the research focuses on estimating the domain of attraction for sub-optimal immunity epidemic models. In the third part of the research, we develop a bond percolation model for community clustered networks with an arbitrarily specified joint degree distribution
New operational matrix of derivative for solving non-linear fractional differential equations via Genocchi polynomials
In this research, new operational method based on Genocchi polynomials for numerical solutions of nonlinear fractional differential equations (NFDEs) is proposed. The Genocchi operational matrix of fractional derivative is first constructed by using some important properties of Genocchi polynomials. These operational matrices together with the collocation method are used to reduce the NFDEs into a system of nonlinear algebraic equations. The error bound for this proposed method is shown. Some examples are given to display the simplicity and accuracy of the proposed technique
Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative
In this article, fractional integro-differential equation (FIDE) of Fredholm type involving right-sided Caputo’s fractional derivative with multi-fractional orders is considered. Analytical expressions of the expansion coefficient ck by Bernoulli polynomials approximation have been derived for both approximation of single- and double-variable function. The Bernoulli polynomials operational matrix of right-sided Caputo’s fractional derivative Pα −;B is derived. By approximating each term in the Fredholm FIDE with right-sided Caputo’s fractional derivative in terms of Bernoulli polynomials basis, the equation is reduced to a system of linear algebraic equation of the unknown coefficients ck. Solving for the coefficients produces the approximate solution for this special type of FIDE
Design for sustainability (D4S) in product development using solidworks software: a case study of redesign a sugar cane extractor machine
The Design for Sustainability (D4S) is a recognized method to produce
sustainable product that embrace three main elements: environment, economic and social. However, the emphasization on the D4S is immature
among industries in Malaysia. The objectives of this study are to propose a
user friendly D4S assessment checklist base on SolidWorks software features
and to implement on a case study. Implementation of this study done by
established a D4S assessment checklist. The checklist consists of mapping
between the sustainability main elements and SolidWorks software. The D4S
case study is redesign a Sugar Cane Extractor Machine based on the proposed
assessment checklist using Solidworks software. The results of study have
shown improvement on all three main elements of sustainability. On the
environment element, the redesign SCEM has been designed with less
environmental impact than original design as following; Carbon Footprint
17.4%, Total Energy Consumed 19.0%, Air Acidification 16.2% and Water
Eutrophication 49.4%. On the economic element, the redesign SCEM has
been designed less material and production cost than original design for
USD28.00 and USD58.50 respectively. On the social element, the redesign
SCEM has been equipped with extra safety cover at exposed area and
ergonomics handles to ease pushing, pulling and lifting operation. In
conclusion, the D4S study has been done successful with consideration on all
three main sustainability
Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method
In this paper, two-dimensional Genocchi polynomials and the Ritz–Galerkin method were developed to investigate the Fractional Diffusion Wave Equation (FDWE) and the Fractional Klein–Gordon Equation (FKGE). A satisfier function that satisfies all the initial and boundary conditions was used. A linear system of algebraic equations was obtained for the considered equation with the help of two-dimensional Genocchi polynomials along with the Ritz–Galerkin method. The FDWE and FKGE, including the nonlinear case, were reduced to solve the linear system of the algebraic equation. Hence, the proposed method was able to greatly reduce the complexity of the problems and provide an accurate solution. The effectiveness of the proposed technique is demonstrated through several examples
Investigation of cutting temperature and cutting force from mist flow pattern in MQL technique
Minimum Quantity Lubrication (MQL) is an alternative method to supply the cutting
fluid in the formation of mist. MQL has proven to reduce machining cost and
increase machining performance. Previous research have stated that machining
performance is affected by the lubricant type, flow rate, the distance between nozzle
and tool tip, and the workpiece material. These important parameters are not reported
in many research documents. MQL is known for its many benefits but no one was
able to prove that the statement is true or ever suggested a systematic procedure to
prove MQL’s efficiency. The effectiveness and the working principle of MQL are
still questionable with very few explanations provided. The present study is about
investigation of cutting temperature and cutting force from mist flow pattern in MQL
technique The MQL nozzle distance and cutting fluid flow pattern are among the
factors that can provide optimum machining performance in term of cutting force
and cutting temperature. The objective of this study is to conduct machining process
using MQL technique with different combination of spray parameters and to
optimize spray parameters for minimum machining temperature and cutting forces.
The four nozzle distances of 3, 6, 7 and 9 mm were selected based on the results
obtained from Phase Doppler Anemometry (PDA). The machining performance was
evaluated under three levels of cutting speed and two levels of feed rate at constant
depth of cut. The cutting force was measured using a set of dynamometer and cutting
temperature using thermal imager. The most suitable mist flow pattern during
machining was the largest spray cone angle supplied under 0.4 MPa input air
pressure. The results obtained from the machining process shows a significant
reduction of cutting force and cutting temperature at the nozzle distance in the range
of 6 to 9 mm under 0.4 MPa input air pressure for larger diameter OD30 nozzle
On the new properties of Caputo–Fabrizio operator and its application in deriving shifted Legendre operational matrix
In this paper, we study the recently introduced Caputo and Fabrizio operator, which this new operator was derived by replacing the singular kernel in the classical Caputo derivative with the regular kernel. We introduce some useful properties based on the definition by Caputo and Fabrizio for a general order n < α < n + 1, n ∈ N. Here, we extend the associated integral of Caputo–Fabrizio sense to n < α < n + 1, n ∈ N. We also find the general formula for the Caputo–Fabrizio operator of (t − a)β . Then, we derive Legendre operational matrix based on this new operator and together with Tau method, we use it to solve the differential equations defined in the Caputo–Fabrizio sense. As far as we know, the operational matrix method has yet been derived or attempted for solving the differential equations in Caputo–Fabrizio sense, while it has been successfully used to solve fractional calculus problems involving the classical Caputo sense. Some numerical examples are given to display the simplicity and accuracy of the proposed technique
Urban rail transit PPPs: Lessons from East Asian cities
Private sector participation in urban rail transit has proliferated in the past two decades. The large metropolises of East Asia have had decades of experience with private sector participation in the provision of heavy metro services. The design of these public–private partnerships (PPP) are varied. The diverse experiences of Tokyo, Hong Kong, Singapore and Beijing contain valuable lessons for other cities. Using a case study approach, this paper discusses three features of urban rail transit developments in the context of East Asian cities, viz., farebox recovery, land value capture mechanisms, and vertical structure of the industry. Super vertical integration between rail transit and real estate development as land value capture strategy to finance urban rail transit has proven to be successful in Japanese cities and Hong Kong. Singapore’s experience illustrates that vertically unbundled PPPs could cut off avenues for cross-subsidisation, reduce information flows as well as economies of scale and scope, introduce principal agent problems, and result in underinvestment in capital stock and maintenance. We conclude that (i) a combination of high farebox recovery ratios and successful land value capture contributed significantly to the development of urban rail transit in East Asia cities; (ii) given the complexities and high costs of heavy metros, the optimal structure is a vertically integrated public-owned and driven system, with the public sector entering into selective partnerships with the private sector where risk sharing is clearly defined and allocated
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