Integro-dierenti Al Equations Research Articles

Non-instantaneous impulsive fractional integro-differential equations with proportional fractional derivatives with respect to another function

"This paper concerns the existence and uniqueness of solutions of non- instantaneous impulsive fractional integro-di erential equations with proportional fractional derivatives with respect to another function. By the aid of the nonlinear alternative of Leray-Schauder type and the Banach contraction mapping principle, the main results are demonstrated. Two examples are inserted to illustrate the applicability of the theoretical results."

Existence of solution for a coupled system of Volterra type integro - dierential equations with nonlocal conditions

In this paper we study the existence of a unique solution for a boundary value prob-lem of a coupled system of Volterra type integro-dierential equations under nonlocal conditions.

On a nonlocal boundary value problem of a coupled system of Volterra functional integro-dierential equations.

In this paper, we study the existence of a unique solution for a nonlocal boundary- value problem of coupled system of Volterra functional integro-dierential equations.

Indirect RBF for High-Order Integro-Differential Equations

Two dierent approaches are applied to solve high-order integro-dierenti al equations (IDEs), based on Radial Basis Functions (RBF). The rst approach, which is called the direct approach (DRBF) is based on dierentiation, and considers the solution as a nite linear combination of RBFs. While the second, the indirect approach (IRBF), is based on integration and considers the highest order derivative of the solution as a nite linear combination of RBFs. The results of this

Fuzzy collocation methods for second- order fuzzy Abel-Volterra integro-differential equations

In this paper we intend to oer new numerical methods to solve the second-order fuzzy Abel-Volterra integro-dierenti al equations under the generalized H-dierentiability . The existence and uniqueness of the solution and convergence of the proposed methods are proved in details and the e- ciency of the methods is illustrated through a numerical example.

Coupled points in ordered generalized metric spaces and application to integro-dierential equations

Abstract In this paper, we prove some coupled fixed point theorems for O-compatible mappings in partially ordered generalized metric spaces under certain conditions to extend and complement the recent fixed point theorems due to Bhaskar and Lakshmikantham [Nonlinear Anal. TMA 65 (2006) 1379 - 1393] and Berinde [Nonlinear Anal. TMA 74 (2011) 7347-7355]. We give some examples to illustrate our results. An application to integro-differential equations is also given.

Existence and controllability of fractional-order impulsive stochastic system with infinite delay

This paper is concerned with the existence and approximate controllability for impulsive fractional-order stochastic innite delay integro-dierenti al equations in Hilbert space. By using Krasnoselskii’s xed point theorem with stochastic analysis theory, we derive a new set of sucient conditions for the approximate controllability of impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.

Existence and controllability of fractional-order impulsive stochastic system with infinite delay

This paper is concerned with the existence and approximate controllability for impulsive fractional-order stochastic innite delay integro-dierenti al equations in Hilbert space. By using Krasnoselskii’s xed point theorem with stochastic analysis theory, we derive a new set of sucient conditions for the approximate controllability of impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.

Fractional Integro-Dierential Equations of Mixed Type with Solution Operator and Optimal Controls

Local and global existence and uniqueness of mild solution for the fractional integro-differential equations of mixed type with delay are proved by using a family of solution operators and the contraction mapping principle on Banach space. TheBolza optimal control problem of a corresponding controlled system is solved. The Gronwall lemma with singular and time lag is derived to be tool for obtaining a priori estimate. In addition, the application to the fractional nonlinear heat equation is shown.

Novel algorithm for simulation of3Dquantum reactive atom-diatom scattering

A new approach is described to the evaluation of the quantum scattering S-matrix in 3D atom-diatom reactive collision. The theory is developed in terms of natural collision coordinates where the coordinate reaction fulfills the same role as a time in a time-dependent scattering formulation. Having written the full wavefunction of the particles system in the coupled-channel representation we have proved that the 3D multi-channel scattering problem can be reduced to the inelastic single-arrangement problem which is described by system of ordinary dierential equations (ODE) of second order. The system of coupled-channel second order ODEs exactly is reduced to the system of integro-dierential equations (IDE) of first order which is solved with the initial conditions. The problem of Koshi for the system of IDEs is proposed to be solved by the method of Runge-Kutta of fourth order. The detailed algorithm for parallel simulation of initial 3D scattering problem is proposed. In result of simulation of IDEs the full wavefunction and all S-matrix elements of reactive transitions and state-to-state cross section are obtained simultaneously without other extra calculations.

Iterative method for solutions and coupled quasi-solutions of nonlinear integro-differential equations of mixed type in Banach spaces

We consider, in this paper, the existence of solutions, coupled minimal and maximal quasi-solutions and iterative approximation of the unique solution for the following initial value problems (IVP) of the nonlinear integro-di erential equations of mixed type in ordered Banach spaces E: u′ = f(t; u; u; Tu; Su); t ∈ I; u(t0) = x0; (1) where I = [t0; t0 + a] (a? 0), x0 ∈E, f∈C[I × E × E × E × E; E] and