The aim of this paper is to introduce a new wavelet method for presenting approximate solutions of multitype variable-order (VO) fractional partial differential equations arising from the modeling of phenomena. In specific, this paper focuses on the numerical solution of the VO-fractional mobile-immobile advection-dispersion equation, Klein Gordon equation and Burgers equation. These equations are

Let M be a Lorentzian manifold and \(\phi\) be a future timelike isometry of M. We use \(\phi\) to construct a concave function \(f_{\phi }\) on M under some conditions on the curvature of timelike and spacelike planes. As a topological application, we characterize the fundamental group of M, when M has positive curvature along timelike planes.

In this paper, we examine the effects of swarm intelligence techniques on the obtaining of numerical solutions of ordinary differential equations (ODEs) with Dirichlet boundary conditions (DBCs) via feed-forward neural networks. Population-based global optimization methods such as artificial bee colony (ABC), ant colony optimization (ACO), gravitational search algorithm (GSA) and particle swarm optimization

Current pagination is devoted to explicate flow attributes of magnetized ferronanoliquid in permeable media in an absorbent channel. Darcy–Forchheimer's relation is utilized to interpret the consideration of porosity. Two types of metallic oxide nanoparticles are used to study hybrid nano-ferrofluids influenced by convective conduction. Mathematical formulation of problem is attained in partial differential

This paper presents a numerical scheme to solve non-local fractional boundary value problems (NFBVPs) through a different implementation of the general form of the reproducing kernel method (RKM) similar to the method eliminating the Gram–Schmidt orthogonalization process to reduce the CPU time. The presented method provides a reliable technique to obtain a reproducing kernel applicable to non-local

This article proposes to solve the traveling wave solutions of the (2+1)-dimensional paraxial wave equation by using modified \(1/G^{\prime}\)-expansion and modified Kudryashov methods. Different types of traveling wave solutions of the (2+1)-dimensional paraxial wave equation have been produced using these methods. Similar and different aspects of the solutions produced by both analytical methods

The Sinc-Galerkin and Sinc-Collocation methods are presented to solve linear Schrodinger equation and obtain the electronic spectrum of linear Schrodinger equations. Some properties of the Sinc methods required for our subsequent development are given and utilized. In sequel, Sinc-Galerkin method is compared with Sinc-Collocation method. Numerical examples are included to demonstrate the validity and

In most standard data envelopment analysis (DEA) models, data are deterministic. However, real-world applications are subject to stochastic data as production costs, which depend on many factors such as environmental and social elements. So, this shortcoming requires the generalization of DEA models to stochastic data. Also, the standard DEA models are often used for positive inputs and outputs, while

A correction to this paper has been published: https://doi.org/10.1007/s40096-021-00415-3

This article gives a numerical solution for solving the two-dimensional nonlinear Fredholm–Volterra partial integro-differential equations with boundary conditions with weakly singular kernels. The collocation method has been used for these operational matrices of the Taylor wavelet along with the Newton method to reduce the given partial integro-differential equation to the system of algebraic equations

The aim of this paper is to establish some fixed point, coincidence point, coupled coincidence point and coupled common fixed point results of an almost generalized \((\phi , \psi , \theta )\)-contractive mappings in ordered b-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. Few examples are illustrated to justify

We inaugurate two concepts, admissible hybrid fuzzy \( {\mathcal{Z}}\)-contractions and hybrid fuzzy \( {\mathcal{Z}}\)-contractions in the bodywork of b-metric spaces and establish sufficient criteria for fuzzy fixed points for such contractions. Nontrivial illustrations are constructed to support the hypotheses of our main notions. From application point of view, a handful of fixed point results

In this study, numerical solution of generalized Rosenau–Kawahara equation with quintic B-spline collocation finite element method has been obtained. First, the generalized Rosenau–Kawahara equation is converted into a coupled differential equation system by the change of variable for the derivative with respect to space variable. Then, the numerical integrations of the resulting system according to

We study the locally risk minimizing approach in a market driven by jump-diffusion stochastic volatility models. We show that the Malliavin calculus, especially a jump-diffusion version of the Clark–Ocone formula, can generate the locally risk minimizing portfolio under weaker restrictions. This means thereafter we do not have to verify the strong condition \(\mathcal {V}(t,s,y)\in C^{1,2,2}\) and

In some processes and systems, undesirable inputs and outputs may be presented along with desirable measures. Undesirable factors play a significant role to calculate the accurate efficiency of Decision Making Units (DMUs). Furthermore, analyzing the impact of a throughput on another throughput in economics and production management gives useful information in order to make a better decision. Therefore

A collocation method based on Bernoulli polynomial is developed to compute the eigenvalues and eigenfunctions of some known fourth-order Sturm-Liouville problems. Properties of Bernoulli matrix method are presented to convert the problem into a system of linear algebraic equations. Error estimation is introduced. The eigenfunctions are calculated for the test problems. A comparison is made with other

This paper proposes two novel families of non-stationary subdivision schemes with a shape parameter of hierarchically and efficiently generating mixed hyperbolic/trigonometric curves of order 3 and 4. An analysis of convergence and smoothness of the proposed schemes is established by using the asymptotic equivalence method. This paper also discusses the bivariate tensor-product subdivision scheme for

Kowalski (Generalized symmetric spaces, Springer, 1980), proved that for Riemannian manifolds \(M_1\) and \(M_2\), if their Riemannian direct product \(M={{M}_{1}}\times {{M}_{2}}\) is Riemannian symmetric spaces, then \(M_1\) and \(M_2\) are Riemannian symmetric spaces. This paper examines this theorem in generalized symmetric spaces, without assuming that each \(M_i\) is simply connected.

In this study, we have modified quintic B-spline base function to use for numerical solution of the Burgers’ equation. For this purpose, the numerical algorithm differential quadrature method and Crank–Nicolson scheme are used for space and time discretization, respectively. To deal with nonlinear terms, they are linearized by using Rubin–Graves technique. To observe the accuracy of the present modification

The goal of the paper is to propose a continuous technique for dealing with first-order linear mixed-type functional differential equations. The approach is established via the employment of the reproducing kernel functions and their nice property. The error results of the tests demonstrate that this approach can give good continuous approximations to the considerable problems.

A perfect 2-coloring of a graph \(\varGamma\) with matrix \(M=\{m_{ij}\}_{i, j=1, 2}\) is a coloring of the vertices \(\varGamma\) with colors called \(\{1, 2\}\) such that the number of vertices of color j adjacent to a fixed vertex of color i is equal to \(m_{ij}\). We state the matrix M is the parameter matrix. Each class of an equitable partition is the vertices with the same color. In this article

In this research article, we connect the \(K^{*}\) iterative process with the class of mappings having property (CSC). We provide some weak and strong convergence theorems regarding the iterative scheme for mappings endowed with property (CSC) in uniformly convex Banach spaces. An example of mappings endowed with property (CSC) is provided which does not satisfy property (C). The \(K^{*}\) iteration

In this manuscript, we investigate the approximate solutions to the tangent nonlinear packaging equation in the context of fractional calculus. It is an important equation because shock and vibrations are unavoidable circumstances for the packaged goods during transport from production plants to the consumer. We consider the fractal fractional Caputo operator and Atangana–Baleanu fractal fractional

Finite element methods have been frequently employed in seeking the numerical solutions of PDEs. In this study, a Galerkin finite element numerical scheme is constructed to explore numerical solutions of the generalized Kuramoto–Sivashinsky (gKS) equation. A quartic trigonometric tension (QTT) B-spline function is adapted as base of the Galerkin technique. The incorporation of B-spline Galerkin in

Gegenbauer, also known as ultra-spherical, polynomials appear often in numerical analysis or interpolation. In the present text we find a recursive formula for and compute the asymptotic behavior of their \(L^2\)-norm.

In recent times, operational matrix methods become overmuch popular. Actually, we have many more operational matrix methods. In this study, a new remodeled method is offered to solve linear Fredholm–Volterra integro-differential equations (FVIDEs) with piecewise intervals using Chebyshev operational matrix method. Using the properties of the Chebyshev polynomials, the Chebyshev operational matrix method

A supporting vector of a matrix A for a certain norm \(\Vert \cdot \Vert \) on \(\mathbb {R}^n\) is a vector x such that \(\Vert x\Vert =1\) and \(\Vert Ax\Vert =\Vert A\Vert =\displaystyle \max _{\Vert y\Vert =1}\Vert Ay\Vert \). In this manuscript, we characterize the existence of supporting vectors in the infinite-dimensional case for both the \(\ell _1\)-norm and the \(\ell _{\infty }\)-norm. Besides

In this article, the numerical solution of glioma, or glioblastomas, which is one of the most aggressive forms of cancer is considered. A heterogeneous nonlinear diffusion logistic density model is taken as the main focus. To obtain the numerical results, three different discretization techniques: Pseudospectral method (PSM) using Chebyshev–Gauss–Lobatto collocation points, method of lines (MoL), and

In this paper, we intend to form certain estimates and identities for the norm of matrix operator from \(\ell _{r}\)-type binomial fractional difference sequence space into \(c, c_{0}, \ell _{\infty }\) and \(\ell _{1}\) sequences spaces. We obtain the necessary and sufficient conditions for some classes of compact operators on \(\ell _{r}\)-type binomial fractional difference sequence space \((1 \le

The combination of Sinc quadrature method and double exponential transformation (DE) is a powerful tool to approximate the singular integrals, and radial basis functions (RBFs) are useful for the higher-dimensional space problem. In this study, we develop a numerical method base on Gaussian-RBF combined with QR-factorization of arising matrix and DE-quadrature Sinc method to approximate the solution

Some discrete distributions generated by stable densities (DGSDs) could be considered as models for describing phenomena arising in bioinformatics. Since probability mass and distribution functions are not in closed forms, simulation studies and real applications of these distributions have not been studied yet. To do this, we need to consider DGSDs as truncated, namely, truncated DGSDs (T-DGSDs).

This work shed light on the solvability of a nonlinear Volterra integral equation in the case where the kernel of this equation is weakly singular. We certainly aim to get a precise solution. This can be achieved by applying a product integration method which is able to construct a nonlinear system. To solve the resulting system, it suffices to employ Broyden’s method. In the sequel, we add a computational

The aim of this study is to offer a compatible numerical technique to solve second-order linear partial integro-differential equations with variable (functional) bounds, including two independent variables, under the initial and/or boundary conditions by using hybrid Hermite and Taylor series. The method converts the presented integro-differential equation to a matrix equation including the unknown

This paper provides a new three-parameter lifetime distribution with increasing and decreasing hazard function. The various statistical properties of the proposed distribution are also discussed. The maximum likelihood method is used for estimating the unknown parameters, and its performance is assessed using Monte-Carlo simulation. Finally, three real data sets are applied to illustrate the application

The present paper focuses on the improving split-step forward methods to solve of stiff stochastic differential equations of Itô type. These methods are based on the exponential modified Euler schemes. We show the convergency of our suggested explicit methods to solution of the corresponding stochastic differential equations in strong sense. For a test equation, mean-square stability of schemes are

In this note for every \(S\)-metric space \((X,S),\) we define a new \(S\)-metric \({S}_{H}\) called Hausdorff S-metric on \(CB(X)\) and show that if \((X,S)\) is complete, \((K\left(X\right), {S}_{H})\) is complete too, where K(X) is the set of all compact nonempty subsets of \(X\) and the notion of weak contraction multi-valued mappings on complete metric spaces (Kritsana Neammanee & Annop Kaewkhao

In this article, we study a class of nonlinear fractional differential equation for the existence and uniqueness of a positive solution and the Hyers–Ulam-type stability. To proceed this work, we utilize the tools of fixed point theory and nonlinear analysis to investigate the concern theory. We convert fractional differential equation into an integral alternative form with the help of the Greens function

This study proposes new statistical tools to analyze the counts of the daily coronavirus cases and deaths. Since the daily new deaths exhibit highly over-dispersion, we introduce a new two-parameter discrete distribution, called discrete generalized Lindley, which enables us to model all kinds of dispersion such as under-, equi-, and over-dispersion. Additionally, we introduce a new count regression

In this study, an effective numerical technique has been introduced for finding the solutions of the first-order integro-differential equations including neutral terms with variable delays. The problem has been defined by using the neutral integro-differential equations with initial value. Then, an alternative numerical method has been introduced for solving these type of problems. The method is expressed

In the present paper, we have established some fixed soft point results on soft S-metric and soft complete S-metric spaces. Instead of contraction or contractive soft mappings, we have considered two arbitrary soft mappings to prove the fixed-point results of soft complete S-metric spaces. We have also show that if the above two soft mappings are coincided, then these results are equivalent to the

In this article, for the first time, a powerful numerical approach, named Sinc–Galerkin algorithm, is employed to explore the thermal performance of moving porous fin subject to nanoliquid flow. Different configurations of‏ ‏nanoparticle such as needle, sphere and disk shapes are considered here. The nonlinear differential equation is introduced and nondimensionalized. The presented governing equation

Block pulse functions are piecewise constant and not smooth enough. Therefore, they offer limited accuracy when used to approximate functions and unable to find highly accurate numerical solutions of fractional differential equations (FDEs). To overcome this problem, we present in this paper a new efficient numerical method for solving FDEs. A hybrid Bernoulli polynomials and block pulse functions

The cost efficiency is one of the types of the used efficiency concepts in the data envelopment analysis (DEA). In the literature of the cost efficiency, the prices are often applied to the units in a fixed and linear form, while in some cases, as the subjects of the savings and observance of the consumption patterns, the prices are usually considered in terms of stepwise (piecewise linear) and not

Exclusive roles have been played by special functions in applied mathematics. It is not astonishing when new classes of special functions are established as the issues associated with special functions are too immense. In this article, the generalized form of hybrid Bessel functions is introduced by using suitable integral transforms and properties of exponential operators. Certain properties including

In this paper, the concept of strong fixed point property of a mapping is defined. The relationship between an approximating fixed point sequence and compactness is studied. The notion of a center set for a mapping is introduced. Some necessary and sufficient conditions for existence of mappings admitting a center set are presented. The results proved herein extend, generalize and improve some well-known

In the present paper, we consider the complete asymptotic expansion of certain exponential-type operators connected with \(2x^{3/2}\). Also, a modification of such exponential-type operators is provided, which preserve the function \(\mathrm{e}^{Ax}\).

In the present paper, a boundary value problem consisting of a Sturm–Liouville equation with boundary conditions dependent on the eigenparameter and discontinuous conditions inside the interval is investigated. We present new Prüfer substitutions and obtain the asymptotic form of eigenvalues, nodal points and nodal lengths. Then, we prove the uniqueness theorem for the solution of the inverse nodal

A mathematical model is realistic to assess a comparative study of nanofluid and hybrid nanofluid flow between two eccentric pipes. Study of nanofluid has been developed recurrently over the earlier era. By taking the nanofluid study in higher level, the researchers tried to use hybrid nanofluid, which was modeled by placing different nanoparticles either in composite or mixture form. The method of

In this study, a Pell–Lucas matrix-collocation method is used to solve a class of Fredholm-type delay integro-differential equations with variable delays under initial conditions. The method involves the basic matrix structures gained from the expansions of the functions at collocation points. Therefore, it performs direct and immediate computation. To test its advantage on the applications, some numerical

Keyfitz entropy index is a new indicator that measures the sensitivity of life expectancy to a change in mortality rate. Understanding the characteristics of this indicator can significantly help life table studies in survival analysis. In this paper, we take a closer look at some mathematical properties of Keyfitz entropy index. First, using theoretical studies we show that in some cases this index

Purpose The main aim of the paper is to introduce the shifted fractional-order Gegenbauer wavelets (SFGWs) and the development of a method for solving fractional nonlinear initial and boundary value problems on a semi-infinite domain. Design/methodology/approach The proposed method is the combination of SFGWs and parametric iteration method. We have derived and constructed the new operational matrices

The radiative MHD unsteady natural flow of Maxwell nanofluid with CNTs (carbon nanotubes) under heat and mass transport past a vertically extended wall subject to slip/no-slip conditions is characterized in this study. Heat generation and thermodiffusion are also considered. The governing equation of flow model of CNTs Maxwell fluid is solved analytical by utilizing the Laplace transform method, and

This paper develops a method for the numerical solution of the nonlinear regularized long wave equation. This method discretizes the unknown solution in two main schemes. The time discretization is accomplished by means of an implicit method based on the \(\theta \)-weighted and finite difference methods, while the spatial discretization is described with the help of the finite difference scheme derived

In this paper, a fractional-order model that describes transmission and control of foot-and-mouth disease is presented and analyzed. The proposed model incorporates two foot-and-mouth disease intervention strategies: vaccination of susceptible animals and quarantine of clinically infected animals. Firstly, the global existence, positivity and boundedness of solutions for the proposed model were proved

In this article, the authors prove some bi-additive \(\sigma\)-random operators inequalities and apply these inequalities, together with the fixed-point technique, to get an approximation of the additive \(\sigma\)-random operators in Menger–Banach (MB) spaces. An approximation of random quasi-\(*\)-multipliers on MB-\(*\)-algebras, associated with the bi-additive \(\sigma\)-random operator inequalities

Existence of solution for functional integral equations of two variables is established in this article under some weaker conditions in a Banach algebra space \(C([0, b]\times [0, b],\mathbb {R}), b>0\) in the form of two operators. We applied the concept of measure of non-compactness (in short, MNC) and Petryshyn fixed point theorem for the operators in the above-mentioned space. For applicability

The concept of return to scale is the ratio of proportional variations in outputs to proportional variations in inputs. A decision maker by determining the returns to scale of a unit can made a decision to limitation or extension of it. The radial models cannot determine the output changes after applying variations in the input vector. So far, the amount of input changes, output changes and efficiency

In this article, the mitigating Internet bottleneck including quadratic–cubic nonlinearity containing the \(\rho\)-derivative has been considered that describes the control of Internet traffic. This equation is analyzed utilizing two integration schemes, videlicet, the extended sinh-Gordon equation expansion technique and improved \(\tan (\Xi /2)\)-expansion technique. Various kinds of traveling wave

In this paper, the numerical solutions of the linear fractional Fredholm–Volterra integro-differential equations have been investigated. For this purpose, Laguerre polynomials have been used to develop an approximation method. Precisely, using the suitable collocation points, a system of linear algebraic equations arises which is resulted by the transformation of the integro-differential equation.

In this article, we work on the existence of solution of generalized fractional integral equations of two variables. To achieve our main objective, we establish a new fixed point theorem using measure of noncompactness and a new contraction operator which generalized the Darbo’s fixed point theorem (DFPT). Also we obtain the corresponding coupled fixed point theorem. Finally we apply this generalized