Differential and Integral Equations This page intentionally left blank DIFFERENTIAL AND INTEGRAL EQUATIONS

Construction of measures of noncompactness of $C^k(Omega)$ and $C^k_0$ and their application to functional integral-differential equations

‎In this paper‎, ‎first‎, ‎we investigate the construction of compact sets of $ C^k$ and $ C_0^k$‎ ‎by proving ``$C^k‎, ‎C_0^k-version$‎" ‎of Arzel`{a}-Ascoli theorem‎, ‎and then introduce new measures of noncompactness on these spaces‎. ‎Finally‎, ‎as an application‎, ‎we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixe...

λ-Symmetry method and the Prelle-Singer method for third-order differential equations

In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry m...

Solving optimal control problems with integral equations or integral equations - differential with the help of cubic B-spline scaling functions and wavelets

In this paper, a numerical method based on cubic B-spline scaling functions and wavelets for solving optimal control problems with the dynamical system of the integral equation or the differential-integral equation is discussed. The Operational matrices of derivative and integration of the product of two cubic B-spline wavelet vectors, collocation method and Gauss-Legendre integration rule for ...

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

The distributional Henstock-Kurzweil integral and measure differential equations

In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in t...