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The purpose of the present work is to propose a wavelet method for the numerical solutions of Caputo–Hadamard fractional differential equations on any arbitrary interval.

The author has modified the CAS wavelets (mCAS) and utilized it for the solution of Caputo–Hadamard fractional linear/nonlinear initial and boundary value problems. The author has derived and constructed the new operational matrices for the mCAS wavelets. Furthermore, The author has also proposed a method which is the combination of mCAS wavelets and quasilinearization technique for the solution of nonlinear Caputo–Hadamard fractional differential equations.

The author has proved the orthonormality of the mCAS wavelets. The author has constructed the mCAS wavelets matrix, mCAS wavelets operational matrix of Hadamard fractional integration of arbitrary order and mCAS wavelets operational matrix of Hadamard fractional integration for Caputo–Hadamard fractional boundary value problems. These operational matrices are used to make the calculations fast. Furthermore, the author works out on the error analysis for the method. The author presented the procedure of implementation for both Caputo–Hadamard fractional initial and boundary value problems. Numerical simulation is provided to illustrate the reliability and accuracy of the method.

Many scientist, physician and engineers can take the benefit of the presented method for the simulation of their linear/nonlinear Caputo–Hadamard fractional differential models. To the best of the author’s knowledge, the present work has never been proposed and implemented for linear/nonlinear Caputo–Hadamard fractional differential equations.

The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method.

The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs.

Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method.

The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

The main purpose of this work is to develop a novel algorithm based on Scale-3 Haar wavelets (S-3 HW) and quasilinearization for numerical simulation of dynamical system of ordinary differential equations.

The first step in the development of the algorithm is quasilinearization process to linearize the problem, and then Scale-3 Haar wavelets are used for space discretization. Finally, the obtained system is solved by Gauss elimination method.

Some numerical examples of fractional dynamical system are considered to check the accuracy of the algorithm. Numerical results show that quasilinearization with Scale-3 Haar wavelet converges fast even for small number of collocation points as compared of classical Scale-2 Haar wavelet (S-2 HW) method. The convergence analysis of the proposed algorithm has been shown that as we increase the resolution level of Scale-3 Haar wavelet error goes to zero rapidly.

To the best of authors’ knowledge, this is the first time that new Haar wavelets Scale-3 have been used in fractional system. A new scheme is developed for dynamical system based on new Scale-3 Haar wavelets. These wavelets take less time than Scale-2 Haar wavelets. This approach extends the idea of Jiwari (2015, 2012) via translation and dilation of Haar function at Scale-3.

You're probably too busy getting the kinks out of your own supply chain to worry about your competitor's. But you should.

The purpose of this paper is to show that there is a wealth of academic literature that qualitatively examines the outsourcing and offshoring from a go/no go perspective. The paper examines the complex “where to outsource” question by applying a quantitative approach called Analytic Hierarchy Process (AHP).

The authors examine a Fortune 500 company's real‐world decision about where to outsource and summarize the current selection process employed by the company. We then apply our AHP model to the company's decision and compare the results.

There are four major findings: the location selection decision is a component of the outsource supplier selection decision; the AHP model effectively manages the complexity of the decision making process, incorporating all decision criteria harmoniously; a method such as AHP, which is able to incorporate both qualitative and quantitative criteria into evaluations, would streamline the decision‐making process; and the AHP process allows firms to look at a portfolio of choices and determine which firms are basically equal in qualifications.

The research implies that: (AHP may be more applicable in these areas by providing a rigorous framework for assessment of qualitative and quantitative factors together; and AHP offers substantial flexibility to accommodate the variety and quantity of decision criteria set forth by the firm.

As firms are more active in pursuing opportunities in global markets, identifying the right offshoring location is critical. The selection process is complex, involving a set of qualitative and quantitative factors and requiring rigorous and careful analysis. Therefore, a scientific method that not only offers flexibility and simplicity, but also simultaneously accommodates a wide variety of decision criteria is invaluable. The research demonstrates that AHP provides these benefits and is an effective technique for analyzing the where‐to‐outsource decision.

The extensive literature review suggests that the majority of the existing works focus on analyzing the go/no‐go decision using a qualitative approach. This paper applies the AHP method to the “where to outsource” question to demonstrate one quantitative approach to this complex decision. Additionally, the paper provides a detailed description of how the AHP method is implemented in analyzing the decision by using a Fortune 500 company's data and information as an example.

In this study, a multi-criteria decision-making (MCDM) approach for evaluating airworthiness factors were presented. The purpose of this study is to develop an acceptable rationale for operational activities in civil and military aviation and for design, production and maintenance activities in the aviation industry that can be used in-flight safety programs and evaluations.

In aviation, while the initial and continuing airworthiness of aircraft is related to technical airworthiness, identifying and minimizing risks for avoiding losses and damages are related to operational airworthiness. Thus, the airworthiness factors in civil and military aviation were evaluated under these two categories as the technical and operational airworthiness factors by the analytic hierarchy process and analytic network process. Three technical and five operational airworthiness criteria for civil aviation, three technical and nine operational airworthiness criteria for military aviation were defined, evaluated, prioritized and compared in terms of flight safety.

The most important technical factor is the “airworthiness status of the aircraft” both in civil (81.9%) and military (77.6%) aviation, which means that aircraft should initially be designed for safety. The most significant operational factors are the “air traffic control system” in civil (30.9%) and “threat” in the military (26.6%) aviation. The differences within factor weights may stem from the design requirements and acceptable safety levels (frequency of occurrences 1 in 10⁷ in military and 1 in 10⁹ in civil aircraft design) of civil and military aircraft with the mission achievement requirements in civil and military aviation operations. The damage acceptance criteria for civil and military aircraft are different. The operation risks are accepted in the military and acceptance of specific tasks and the risk levels can vary with aircraft purpose and type.

This study provides an acceptable rationale for safety programs and evaluations in aviation activities. The results of this study can be used in real-world airworthiness applications and safety management by the aviation industry and furthermore, critical factor weights should be considered both in civil and military aviation operations and flights. The safety levels of airlines with respect to our airworthiness factor weights or the safety level of military operations can be computed.

This is the first study considering technical and operational airworthiness factors as an MCDM problem. Originality and value of this paper are defining critical airworthiness factors for civil and military aviation, ranking these factors, revealing the most important ones and using MCDM methods for the evaluations of airworthiness factors for the first time. In civil aviation flight safety is the basic tenet of airworthiness activities in risk analysis, on the other hand in military aviation high levels of risks are to be avoided in peace training or operational tasks. However, even high risks have to be accepted during the war, if the operational requirements impose, as mission achievement is vital. The paper is one of a kind on airworthiness evaluations for flight safety.

The purpose of the present work is to introduce a wavelet method for the solution of linear and nonlinear psi-Caputo fractional initial and boundary value problem.

The authors have introduced the new generalized operational matrices for the psi-CAS (Cosine and Sine) wavelets, and these matrices are successfully utilized for the solution of linear and nonlinear psi-Caputo fractional initial and boundary value problem. For the nonlinear problems, the authors merge the present method with the quasilinearization technique.

The authors have drived the orthogonality condition for the psi-CAS wavelets. The authors have derived and constructed the psi-CAS wavelets matrix, psi-CAS wavelets operational matrix of psi-fractional order integral and psi-CAS wavelets operational matrix of psi-fractional order integration for psi-fractional boundary value problem. These matrices are successfully utilized for the solutions of psi-Caputo fractional differential equations. The purpose of these operational matrices is to make the calculations faster. Furthermore, the authors have derived the convergence analysis of the method. The procedure of implementation for the proposed method is also given. For the accuracy and applicability of the method, the authors implemented the method on some linear and nonlinear psi-Caputo fractional initial and boundary value problems and compare the obtained results with exact solutions.

Since psi-Caputo fractional differential equation is a new and emerging field, many engineers can utilize the present technique for the numerical simulations of their linear/non-linear psi-Caputo fractional differential models. To the best of the authors’ knowledge, the present work has never been introduced and implemented for psi-Caputo fractional differential equations.

The purpose of this paper is to develop a new method based on operational matrices of Bernoulli wavelet for solving linear stochastic Itô-Volterra integral equations, numerically.

For this aim, Bernoulli polynomials and Bernoulli wavelet are introduced, and their properties are expressed. Then, the operational matrix and the stochastic operational matrix of integration based on Bernoulli wavelet are calculated for the first time.

By applying these matrices, the main problem would be transformed into a linear system of algebraic equations which can be solved by using a suitable numerical method. Also, a few results related to error estimate and convergence analysis of the proposed scheme are investigated.

Two numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. All of the numerical calculation is performed on a personal computer by running some codes written in MATLAB software.

This paper aims to present a new method for the approximate solution of two-dimensional nonlinear Volterra–Fredholm partial integro-differential equations with boundary conditions using two-dimensional Chebyshev wavelets.

For this purpose, an operational matrix of product and integration of the cross-product and differentiation are introduced that essentially of Chebyshev wavelets. The use of these operational matrices simplifies considerably the structure of the computation used for a set of the algebraic system has been obtained by using the collocation points and solved.

Theorem for convergence analysis and some illustrative examples of using the presented method to show the validity, efficiency, high accuracy and applicability of the proposed technique. Some figures are plotted to demonstrate the error analysis of the proposed scheme.

This paper uses operational matrices of two-dimensional Chebyshev wavelets and helps to obtain high accuracy of the method.

In this article, the authors aims to introduce a novel Vieta–Lucas wavelets method by generalizing the Vieta–Lucas polynomials for the numerical solutions of fractional linear and non-linear delay differential equations on semi-infinite interval.

The authors have worked on the development of the operational matrices for the Vieta–Lucas wavelets and their Riemann–Liouville fractional integral, and these matrices are successfully utilized for the solution of fractional linear and non-linear delay differential equations on semi-infinite interval. The method which authors have introduced in the current paper utilizes the operational matrices of Vieta–Lucas wavelets to converts the fractional delay differential equations (FDDEs) into a system of algebraic equations. For non-linear FDDE, the authors utilize the quasilinearization technique in conjunction with the Vieta–Lucas wavelets method.

The purpose of utilizing the new operational matrices is to make the method more efficient, because the operational matrices contains many zero entries. Authors have worked out on both error and convergence analysis of the present method. Procedure of implementation for FDDE is also provided. Furthermore, numerical simulations are provided to illustrate the reliability and accuracy of the method.

Many engineers or scientist can utilize the present method for solving their ordinary or Caputo–fractional differential models. To the best of authors’ knowledge, the present work has not been used or introduced for the considered type of differential equations.