Solutions Of Functional Integral Equation Research Articles

Existence of solution of functional integral equations by measure of noncompactness and sinc interpolation to find solution

Existence of solution of functional integral equations by measure of noncompactness and sinc interpolation to find solution

An existence theorem for nonlinear functional Volterra integral equations via Petryshyn's fixed point theorem

<abstract><p>Using the method of Petryshyn's fixed point theorem in Banach algebra, we investigate the existence of solutions for functional integral equations, which involves as specific cases many functional integral equations that appear in different branches of non-linear analysis and their applications. Finally, we recall some particular cases and examples to validate the applicability of our study.</p></abstract>

Applications of Measure of Noncompactness and Operator Type Contraction for Existence of Solution of Functional Integral Equations

The objective of this paper is to study the existence of solution of functional integral equations using a measure of noncompactness argument combined with generalized coupled fixed point theorem with the help of operator type contraction mapping in Banach spaces. We present an example to illustrate our results.

Some New Generalization of Darbo’s Fixed Point Theorem and Its Application on Integral Equations

In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Banach Algebra, and also illustrate the results with the help of an example.

Existence of tripled fixed points and solution of functional integral equations through a measure of noncompactness

In this paper, we propose fixed point results through the notion of a measure of noncompactness and give a generalization of a Darbo’s fixed point theorem. We also prove some new tripled fixed point results via a measure of noncompactness for a more general class of functions. Our results generalize and extend some comparable results in the literature. Further, we apply the obtained fixed point theorems to prove the existence of solutions for a general system of non-linear functional integral equations. In the end, an example is given to illustrate the validity of our results.

On solution of functional integral equation of fractional order

The aim of this paper is to investigate existence and stability of the solution of the functional integral equations of fractional order arising in physics, mechanics and chemical reactions. These equations are considered in the Banach space of real functions defined, continuous and bounded on an unbounded interval R+. The main tools used in our considerations are the concept of a measure of noncompactness and the classical Schauder fixed point theorem. Also, the numerical method is employed successfully for solving these functional integral equations of fractional order.

Existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on [formula omitted

Let Lp(R+) denote the space of Lebesgue integrable functions on R+ with the standard norm∥x∥p=(∫0∞|x(t)|pdt)1p.First, we define a new measure of noncompactness on the spaces Lp(R+) (1 ≤ p < ∞). In addition, we study the existence of entire solutions for a class of nonlinear functional integral equations of convolution type using Darbo’s fixed point theorem, which is associated with the new measure of noncompactness. We provide some examples to demonstrate that our results are applicable whereas the previous results are not.

On Attractivity and Positivity of Solutions for Functional Integral Equations of Fractional Order

We investigate a class of functional integral equations of fractional order given byx(t)=q(t)+f1(t,x(α1(t)),x(α2(t)))+(f2(t,x(β1(t)),x(β2(t)))/Γ(α))×∫0t(t−s)α−1f3(t,s,x(γ1(s)),x(γ2(s)))ds: sufficient conditions for the existence, global attractivity, and ultimate positivity of solutions of the equations are derived. The main tools include the techniques of measures of noncompactness and a recent measure theoretic fixed point theorem of Dhage. Our investigations are placed in the Banach space of continuous and bounded real-valued functions defined on unbounded intervals. Moreover, two examples are given to illustrate our results.

Numerical solution of functional integral equations by the variational iteration method

In the present article, we apply the variational iteration method to obtain the numerical solution of the functional integral equations. This method does not need to be dependent on linearization, weak nonlinearity assumptions or perturbation theory. Application of this method in finding the approximate solution of some examples confirms its validity. The results seem to show that the method is very effective and convenient for solving such equations.

On local attractivity of solutions of a functional integral equation of fractional order with deviating arguments

In this paper, we study the existence of solutions of a nonlinear functional integral equation of fractional order with deviating arguments. This equation is considered in the Banach space of real functions defined, continuous and bounded on an unbounded interval. Moreover, we show that solutions of this integral equation are locally attractive. An example is provided to illustrate the theory.

On the existence of solutions of functional integral equation of Urysohn type

In this paper we introduce a brief historical note about the study of the existence of solutions of functional integral equations. Hence we prove the existence of monotonic solutions of the functional integral equation of Urysohn type. The technique rely on the concept of measure of noncompactness and its associated Darbo fixed point theorem.

Integrable solutions of a nonlinear functional integral equation on an unbounded interval

In this paper we prove the existence of integrable solutions of a generalized functional-integral equation, which includes many key integral and functional equations that arise in nonlinear analysis and its applications. This is achieved by means of an improvement of a Krasnosel’skii type fixed point theorem recently proved by K. Latrach and the author. The result presented in this paper extends the corresponding result of [J. Banas, A. Chlebowicz, On existence of integrable solutions of a functional integral equation under Carathéodory condition, Nonlinear Anal. (2008) doi:10.1016/j.na.2008.04.020]. An example which shows the importance and the applicability of our result is also included.

Numerical solutions of functional integral equations

In this paper, we give a more general definition of integral equations of the second and first kind which are called functional integral equations. Fredholm and Volterra integral equations are special type of these equations. We derive an expansion method to treat these equations. Finally, we introduce numerical examples and conclusion.

Numerical solutions for functional integral equations with state-dependent delay

Existence and uniqueness theorems are given for a family of functional integral equations with a state-dependent delay. Convergence criteria for a family of numerical methods for these equations are also given. Numerical results are included.

Numerical solutions for functional integral equations

Convergence criteria are given for a family of numerical methods for functional integral equations with delay. Several numerical methods are compared

Uniqueness and global convergence of successive approximations for solutions of functional integral equations with infinite delay

Uniqueness and global convergence of successive approximations for solutions of functional integral equations with infinite delay

Successive approximations for solutions of functional integral equations

in a Banach space X, where r > 0, J= [o, b] or ICJ, b) and the integral is in the sense of Bochner. This equation is a unification and extension of a nonlinear Volterra integral equation and a functional differential equation of retarded type. Indeed, if in (1.1) the function f satisfies that f(f) --S(a) for t E J, then it is reduced to a functional differential equation in a Banach space. De Balasi and Myjak (21 gave a global convergence version of successive approximations to solutions for such reduced equations under the assumption that g is Lipschitz continuous and bounded. If, in addition, r = 0 then (1.1) is reduced to an ordinary differential equation. For this, Vidossich 161 discussed the global convergence of Picard’s successive approximations to solutions under some less restrictive conditions on g. The main purpose of this paper is to extend Vidossich’s results to the solutions of Eq. (1.1). Our conditions made on g are similar to what Miller [4] and Artzstein [ 1 ] made for the integral equation (1.1) with r = 0 and what Vidossich (61 made for the ordinary differential equation referred above.