Published in Open Mathematics
We study a linear boundary value problem for systems of essentially loaded differential equations with an integro-multipoint condition. We make use of the numerical implementation of the Dzhumabaev parametrization method to obtain the desired result, which is well supported by two numerical examples.
Published in International Journal of Applied and Computational Mathematics
This paper gives and justifies a practical approach for solving fuzzy singular integro-differential equations. First, by using different techniques, we show that solutions to two types of fuzzy singular integro-differential equations exist and are unique: Picard’s theorem for logarithmic kernels and Arzelà–Ascoli theorem for Cauchy ones. Then, util...
Published in Fractional Calculus and Applied Analysis
The identification problem for system with distributed-order derivative was considered. The order-weight distribution was approximated by piecewise linear functions. Then the discretized order-weight distribution was solved in frequency domain by using the least square technique based on the Moore-Penrose inverse matrix. Finally, five representativ...
Published in Applied Mathematics and Mechanics
In this paper, we propose general strain- and stress-driven two-phase local/nonlocal piezoelectric integral models, which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures. The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitu...
Published in Computational and Applied Mathematics
In this paper, we focus on an efficient convergent method to solve the linear fractional delay integro-differential equations. We first convert the equation into an equivalent system by replacing the delay function in the sections containing delay in two intervals before the delay time and after the delay time. In the next step, we discretize the n...
Published in Computational and Applied Mathematics
In this article, a polynomial collocation method for the numerical solution of fuzzy Fredholm integro-differential equation has been presented. The function space and the operator properties have been developed, which helps to develop the convergence analysis of this method. The convergence analysis has been given in the form of different theorems ...
Published in Computational and Applied Mathematics
In this paper, a nonlinear Volterra integro-differential equation with Caputo fractional derivative, multiple kernels, and multiple constant delays is considered. The aim of this paper is to investigate qualitative properties of solutions of this equation such as uniform stability, asymptotic stability, and Mittag-Leffler stability of the zero solu...
Published in Computational and Applied Mathematics
This paper addresses a computational technique for the numerical solutions of nonlinear distributed-order fractional boundary value equations with singular coefficients. The proposed strategy is based on the shifted Legendre-series expansion and the composite midpoint quadrature rule. Moreover, a collocation technique is utilized to reduce the unde...
Published in Journal of Scientific Computing
In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odds...
Published in Boletín de la Sociedad Matemática Mexicana
In the present paper, the differential, integro-differential and partial differential equations satisfied by the 2-iterated 2D Appell polynomials are obtained via the factorization method. Results for certain 2D hybrid families related to the Appell polynomials are derived. Further, corresponding results for certain mixed type and 2-iterated member...
