In this paper, a high-order compact finite difference method (CFDM) with an operator-splitting technique for solving the 3D time-fractional diffusion equation is considered. The Caputo–Fabrizio time operator is evaluated by the \(L_1\) approximation, and the second-order space derivatives are approximated by the compact CFDM to obtain a discrete scheme. Alternating direction implicit method (ADI) is

It is well known the connection between the growth of the Schwarzian with both the univalence [see Beardon and Gehring (Comment Math Helv 55: 50–64, 1980), Nehari (Bull Am Math Soc 55:545–551, 1949), Ovesea (Novi Sad J Math 26(1):69–76, 1996)] and the quasiconformal extension of the function [see Ahlfors and Weill (Proc Am Math Soc 13:975–978, 1962), Osgood (Old and new on the Schwarzian derivative

This paper studies an investor’s optimal investment, optimal net debt ratio with collateral security and optimal consumption plan in an economy that faces both diffusion and jump risks. The underlying assets are tangible and intangible assets. There have been major challenges of quantifying intangible assets. In this paper, we assume that the price of our intangible asset follows a jump-diffusion process

This work introduces a direct method based on orthonormal Bernstein polynomials wavelet bases, to present a stable algorithm for numerical inversion of a system of generalized Abel integral equations. The application of all the currently existing numerical inversion methods was strictly limited to only one portion of the generalized Abel integral equations. The proposed method is quite accurate, and

Data envelopment analysis (DEA) is a model for measuring the efficiency of decision-making units (DMUs). The majority of DEA models suffer from drawbacks, in particular, changes in the weights of inputs and outputs. Consequently, the efficiency of DMUs is measured with different weights and so it is important to establish how to evaluate all DMUs using a common weight to optimize their efficiency at

The \((4+1)\)-dimensional Fokas (4DFK) equation is explicitly written out by means of the linearized operator of the 4DFK equation after introducing an additional auxiliary variable. Based on the bilinear form, bilinear Bäcklund transformations consisting of three bilinear equations are provided. A new class of lump solutions is given and analyzed using the extremum theory of multivariate function

In the present study, the problem of simulating a non-Newtonian and two-dimensional blood flow in a flexible stenosed artery is examined by an implicit finite difference method. The streaming blood in the human artery is represented as a micropolar fluid. The governing non-Linear partial differential equations are modeled in cylindrical coordinates system and following a suitable radial coordinate

An improved derivative-free trust-region method to solve systems of nonlinear equations in several variables is presented, combined with the Wolfe conditions to update the trust-region radius. We believe that producing step-sizes by the Wolfe conditions can control the trust-region radius. The new algorithm for which strong global convergence properties are proved is robust and efficient enough to

In this paper, we consider a bivariate nonlinear Fredholm integral equation of the second kind. Then an approximate solution for some of these problems is investigated. To determine the aimed solution, the hybrid of 2D block-pulse functions with Chebyshev polynomials basis with the operational matrices is applied. In this work, we generalize the operational matrices stated by Behbahani (J Basic Appl

In this paper, a new and applied concept of topological spaces based upon relations is introduced. These topological spaces are called R-topological spaces and SR-topological spaces. Some of the properties of these spaces and their relationship with the initial topological space are verified. Moreover, some of their applications for example in fixed point theory, functional analysis, \(C^*\)-algebras

In this paper, complex reproducing kernel Hilbert spaces and their reproducing kernels are introduced. The reproducing kernel is constructed by combining Gaussian radical basis function kernel and spline kernel. In the spaces, using the related theory, a novel numerical method is developed to solve Schröinger equations. The present method is a meshless method and does not require connection between

Multi-objective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multi-objective linear plus linear fractional

In this paper, we present the complex Rolle’s and Mean Value Theorems for \(\alpha\)-holomorphic functions and give some related results and applications of these theorems.

A method based on B-splines has been introduced for the solution of second-order nonlinear hyperbolic equation in 2-dimensions subject to appropriate initial and Dirichlet boundary conditions. We first convert the second-order equation into a system of first-order partial differential equations. Then, collocation of bi-cubic B-splines is used to discretize spatial variables and their derivatives to

Neutrosophy consists of neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalisation of classical sets, fuzzy set, intuitionistic fuzzy set, etc. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena where it is necessary

In this work, we propose a numerical framework for solving a class of Lienard’s equation. This equation arises in the development of radio and vacuum tube technology. The spatial approximation is based on the Bernoulli collocation method in which the shifted Chebyshev collocation points are used as collocation nodes. The operational matrix of derivatives of Bernoulli is introduced. The matrix together

Here, we have studied the ideas of (s, t)-\(g_{\rho }\) and (s, t)-\(\lambda _{\rho }\)-closed sets \((s,t=1,2;\,\, s\not =t)\) and pairwise \(\lambda\)-closed sets in a generalized bitopological space \((X,{\rho_{1}}, {\rho_{2}})\). We have investigated the properties on some new separation axioms namely pairwise \(T_\frac{1}{4}\), pairwise \(T_\frac{3}{8}\), pairwise \(T_\frac{5}{8}\) and have established

The ambition of this paper is to construct fixed point theorems fulfilling a generalized locally F-contractive multivalued mapping on a closed ball in complete b-metric-like space. Example and application are given to show the novelty of our results. Our results combine, extend and infer several comparable results in the existing literature.

Direct methods are applied to solve linear time-varying delay systems based on vector forms of block-pulse functions (BPFs) and triangular functions (TFs). Operational matrices of integration of BPFs and TFs are applied to transform linear time-varying delay systems to a linear set of algebraic equations. Further, some numerical examples are provided to indicate reliability and the accuracy of these

Nowadays, certain problems in automata theory, manufacturing systems, telecommunication networks, parallel processing systems and traffic control are intimately linked with linear systems over tropical semirings. Due to non-invertibility of matrices—except monomial matrices—over certain semirings, we cannot generally take advantage of having the inverse of the coefficient matrix of a system to solve

Detection of spam and non-spam emails is considered a great challenge for email service providers and users alike. Spam emails waste the Internet traffic and also contain malicious links that mostly direct users to phishing webpages. Another challenge of spams is their role in spreading malware on the network, further emphasizing the need for their detection. Despite the application of data mining

In this paper, we discuss and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then go over a specific version of Cramer’s rule which is also related to the pseudo-inverse of the system matrix. In these two methods, the constant vector plays an implicit role in solvability of the system. Another

In this article, the authors proposed Chebyshev pseudospectral method for numerical solutions of two-dimensional nonlinear Schrodinger equation with fractional-order derivative in both time and space. Fractional-order partial differential equations are considered as generalizations of classical integer-order partial differential equations. The proposed method is established in both time and space to

We show that the classical Marsden–Weinstein Reduction theorem for Hamiltonian systems with symmetries is still true for contact–symplectic pairs.