Optimal control of system governed by nonlinear volterra integral and fractional derivative equations

AbstractThis work presents a novel formulation for the numerical solution of optimal control problems related to nonlinear Volterra fractional integral equations systems. A spectral approach is implemented based on the new polynomials known as Chelyshkov polynomials. First, the properties of these polynomials are studied to solve the aforementioned problems. The operational matrices and the Galerkin method are used to discretize the continuous optimal control problems. Thereafter, some necessary conditions are defined according to which the optimal solutions of discrete problems converge to the optimal solution of the continuous ones. The applicability of the proposed approach has been illustrated through several examples. In addition, a comparison is made with other methods for showing the accuracy of the proposed one, resulting also in an improved efficiency

Is the compact binary coalescence, GW190425, a strange quark star?

In this study, the effects of different QCD models in the structure of strange quark star (SQS) are investigated. In these models, the running coupling constant has a finite value in the infrared region of energy. By imposing some constraints on the strange quark matter (SQM) and by exploiting the analytic and background perturbation theories, the equations of states for the SQM are obtained. Then, the properties of SQSs in general relativity are evaluated. By using component masses of GW190425 as well as some conversion relations between the baryonic mass and the gravitational mass, the remnant mass of GW190425 is obtained. Our results for the maximum gravitational mass of SQS are then compared with the remnant mass of GW190425. The results indicate that the obtained maximum gravitational masses are comparable to the remnant mass of GW190425. Therefore, it is proposed that the remnant mass of GW190425 might be a SQS.Comment: 8 pages, 5 figures, 4 tables. Added two section

Spatial autocorrelation and epidemiological survey of visceral leishmaniasis in an endemic area of Azerbaijan region, the northwest of Iran.

Visceral leishmaniasis (VL) is a common infectious disease that is endemic in Iran. This study aimed to investigate the spatial autocorrelation of VL in the northwest of Iran. In this cross-sectional study, the data of all patients were collected in 2009-2017 and analyzed by SPSS23 and Moran's and General G Index. The MaxEnt3.3.3 software was used to determine the ecological niche. A big hot spot area was identified in five counties in the northwest of Iran. More than 70% of the cases were reported from these regions, and the incidence rate increased in the northwest of Iran from 2013 to 2017. Seasonal rainfall and average daily temperature were the most important climate variables affecting the incidence of VL in this region (p < 0.05). Therefore, it can be concluded that VL in the northwest of Iran is expanding to new areas along the border with the Republic of Azerbaijan, and the northeastern section of this region is a high-risk area

A Galerkin approach for fractional delay differential equations using hybrid Chelyshkov basis functions

This study proposes a numerical technique based on a hybrid of block-pulse functions and Chelyshkov polynomials to solve fractional delay differential equations. The Galerkin approach transforms the solution of fractional delay differential equations into a system of algebraic equations using the fractional operational matrix of integration for these hybrid functions. The suggested method's accuracy and efficiency are demonstrated using numerical examples

Comparison Between Protein-Protein Interaction Networks CD4 + T and CD8 + T and a Numerical Approach for Fractional HIV Infection of CD4 + T Cells

This research examines and compares the construction of protein-protein interaction (PPI) networks of CD4+ and CD8+T cells and investigates why studying these cells is critical after HIV infection. This study also examines a mathematical model of fractional HIV infection of CD4+T cells and proposes a new numerical procedure for this model that focuses on a recent kind of orthogonal polynomials called discrete Chebyshev polynomials. The proposed scheme consists of reducing the problem by extending the approximated solutions and by using unknown coefficients to nonlinear algebraic equations. For calculating unknown coefficients, fractional operational matrices for orthogonal polynomials are obtained. Finally, there is an example to show the effectiveness of the recommended method. All calculations were performed using the Maple 17 computer code