scholarly journals Semilinear Volterra Integrodifferential Problems with Fractional Derivatives in the Nonlinearities

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Mokhtar Kirane ◽  
Milan Medveď ◽  
Nasser-eddine Tatar
Keyword(s):  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Mild Solutions ◽  
Second Order ◽  
Classical Solutions ◽  
Volterra Integrodifferential Equation

A second-order semilinear Volterra integrodifferential equation involving fractional time derivatives is considered. We prove existence and uniqueness of mild solutions and classical solutions in appropriate spaces.

scholarly journals ON A SECOND-ORDER DIFFERENTIAL PROBLEM WITH FRACTIONAL DERIVATIVES OF ORDER GREATER THAN ONE

2013 ◽  
Vol 18 (1) ◽  
pp. 53-65
Author(s):  
Nasser-eddine Tatar
Keyword(s):  
Existence And Uniqueness ◽  
Present Author ◽  
Fractional Derivatives ◽  
Second Order ◽  
Classical Solutions ◽  
Differential Problem ◽  
Abstract Problem ◽  
Integer Order ◽  
First Order ◽  
Derivatives Of

A second-order abstract problem with derivatives of non-integer order is investigated. The nonlinearity involves fractional derivatives between 1 and 2. Existence and uniqueness of mild and classical solutions are established in appropriate spaces. This work extends similar works with or without a derivative of first order and also a work of the present author, where the order of the derivatives were between 0 and 1.

scholarly journals THE NON-LOCAL CAUCHY PROBLEM FOR SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT

2001 ◽  
Vol 44 (1) ◽  
pp. 63-70 ◽  
Author(s):  
K. Balachandran ◽  
M. Chandrasekaran
Keyword(s):  
Cauchy Problem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Subject Classification ◽  
Classical Solutions ◽  
Deviating Argument ◽  
Primary 34K05 ◽  
Non Local

AbstractThe aim of this paper is to prove the existence and uniqueness of mild and classical solutions of the non-local Cauchy problem for a semilinear integrodifferential equation with deviating argument. The results are established by using the method of semigroups and the contraction mapping principle. The paper generalizes certain results of Lin and Liu.AMS 2000 Mathematics subject classification: Primary 34K05; 34K30

scholarly journals Existence and uniqueness of mild and strong solutions of nonlinear volterra integrodifferential equations in Banach spaces

2010 ◽  
Vol 43 (3) ◽  
Author(s):  
H. L. Tidke ◽  
M. B. Dhakne
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Semigroup Theory ◽  
Strong Solutions ◽  
Banach Fixed Point Theorem ◽  
Volterra Integrodifferential Equation

AbstractIn this paper we prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra integrodifferential equation with nonlocal condition. Our analysis is based on semigroup theory and Banach fixed point theorem and inequalities are established by Gronwall and B. G. Pachpatte.

scholarly journals ON FRACTIONAL VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH FRACTIONAL INTEGRABLE IMPULSES

2019 ◽  
Vol 24 (3) ◽  
pp. 457-477 ◽  
Author(s):  
Sagar T. Sutar ◽  
Kishor D. Kucche Kucche
Keyword(s):  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Integrodifferential Equations ◽  
Compact Interval ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Volterra Integrodifferential Equation

We consider a class of nonlinear fractional Volterra integrodifferential equation with fractional integrable impulses and investigate the existence and uniqueness results in the Bielecki’s normed Banach spaces. Further, Bielecki-Ulam type stabilities have been demonstrated on a compact interval. A concrete example is provided to illustrate the outcomes we acquired.

scholarly journals Polynomial spline collocation methods for second-order Volterra integrodifferential equations

2004 ◽  
Vol 2004 (56) ◽  
pp. 3011-3022 ◽  
Author(s):  
Edris Rawashdeh ◽  
David Mcdowell ◽  
Leela Rakesh
Keyword(s):  
Integrodifferential Equation ◽  
Polynomial Spline ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Collocation Methods ◽  
Spline Collocation ◽  
Initial Value ◽  
Volterra Integrodifferential Equation

We have presented a method for the construction of an approximation to the initial-value second-order Volterra integrodifferential equation (VIDE). The polynomial spline collocation methods described here give a superconvergence to the solution of the equation.

scholarly journals On stochastic integrodifferential equations via non-linear integral contractors II

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 81-92 ◽  
Author(s):  
Miljana Jovanovic ◽  
Svetlana Jankovic
Keyword(s):  
Lipschitz Condition ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Theorems ◽  
Volterra Integrodifferential Equation ◽  
Subject Classifications ◽  
Non Linear ◽  
Random Integral ◽  
Linear Integral ◽  
Mathematics Subject Classifications

The present paper represents a continuation of paper [4], in which the existence and uniqueness problems for a general Ito-Volterra integrodifferential equation are investigated by using the concept of a non-linear random integral contractor. Since the Lipschitz condition and the random integral contractor for the coefficients of the considered equation, in general, cannot be compared, the notions of the modified Lipschitz condition and modified integral contractor are introduced on some function spaces, as well as the conditions of their equivalence. Some existence and uniqueness theorems are also given. 2010 Mathematics Subject Classifications. 60H20. .

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