Averaging of fuzzy differential equations on a finite interval

2012 ◽  
Vol 14 (4) ◽  
pp. 547-559
Author(s):  
A. V. Plotnikov ◽  
T. A. Komleva
Keyword(s):  
Differential Equations ◽  
Finite Interval

scholarly journals Computer Simulation and Iterative Algorithm for Approximate Solving of Initial Value Problem for Riemann-Liouville Fractional Delay Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 477
Author(s):  
Snezhana Hristova ◽  
Kremena Stefanova ◽  
Angel Golev
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Finite Interval ◽  
Initial Value ◽  
Monotone Iterative ◽  
Practical Usefulness ◽  
Fractional Delay ◽  
Fractional Differential ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

The main aim of this paper is to suggest an algorithm for constructing two monotone sequences of mild lower and upper solutions which are convergent to the mild solution of the initial value problem for Riemann-Liouville fractional delay differential equation. The iterative scheme is based on a monotone iterative technique. The suggested scheme is computerized and applied to solve approximately the initial value problem for scalar nonlinear Riemann-Liouville fractional differential equations with a constant delay on a finite interval. The suggested and well-grounded algorithm is applied to a particular problem and the practical usefulness is illustrated.

scholarly journals Initial value problems for first order impulsive integro-differential equations of Volterra type in Banach spaces

2007 ◽  
Vol 5 (1) ◽  
pp. 9-26 ◽  
Author(s):  
Jiang Zhu ◽  
Yajuan Yu ◽  
Vasile Postolica
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Initial Value Problems ◽  
Finite Interval ◽  
Estimation Method ◽  
Partial Ordering ◽  
Initial Value ◽  
Volterra Type ◽  
First Order ◽  
Noncompactness Measure

In this paper, we use a new method and combining the partial ordering method to study the existence of the solutions for the first order nonlinear impulsive integro-differential equations of Volterra type on finite interval in Banach spaces and for the first order nonlinear impulsive integro-differential equations of Volterra type on infinite interval with infinite number impulsive times in Banach spaces. By introducing an interim space and using progressive estimation method, some restrictive conditions on impulsive terms, used before, such as, prior estimation, noncompactness measure estimations are deleted.

Iterative techniques with computer realization for initial value problems for Riemann–Liouville fractional differential equations

2020 ◽  
Vol 26 (1) ◽  
pp. 21-47 ◽  
Author(s):  
Ravi Agarwal ◽  
A. Golev ◽  
S. Hristova ◽  
D. O’Regan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Finite Interval ◽  
Lower And Upper Solutions ◽  
Successive Approximations ◽  
Initial Value ◽  
Practical Usefulness ◽  
Computer Environment ◽  
Fractional Differential ◽  
The Given

AbstractThe main aim of this paper is to suggest some algorithms and to use them in an appropriate computer environment to solve approximately the initial value problem for scalar nonlinear Riemann–Liouville fractional differential equations on a finite interval. The iterative schemes are based on appropriately defined lower and upper solutions to the given problem. A number of different cases depending on the type of lower and upper solutions are studied and various schemes for constructing successive approximations are provided. The suggested schemes are applied to some problems and their practical usefulness is illustrated.

scholarly journals Hyers–Ulam stability of impulsive Volterra delay integro-differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
D. A. Refaai ◽  
M. M. A. El-Sheikh ◽  
Gamal A. F. Ismail ◽  
Bahaaeldin Abdalla ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Integral ◽  
Finite Interval ◽  
Ulam Stability ◽  
First Order ◽  
Fixed Point Approach ◽  
Different Types ◽  
The Stability ◽  
Stability Results

AbstractThis paper discusses different types of Ulam stability of first-order nonlinear Volterra delay integro-differential equations with impulses. Such types of equations allow the presence of two kinds of memory effects represented by the delay and the kernel of the used fractional integral operator. Our analysis is based on Pachpatte’s inequality and the fixed point approach represented by the Picard operators. Applications are provided to illustrate the stability results obtained in the case of a finite interval.

On a class of integro-differential equations

1944 ◽  
Vol 40 (3) ◽  
pp. 199-211 ◽  
Author(s):  
H. R. Pitt
Keyword(s):  
Differential Equations ◽  
Bounded Variation ◽  
Finite Interval ◽  
Image Position

We are concerned in this paper with linear integro-differential equations of the form*andwhere kr(y) are given functions with bounded variation in any finite interval, g(x) is known, and f(x) is to be determined.

scholarly journals Nonautonomous Differential Equations in Banach Space and Nonrectifiable Attractivity in Two-Dimensional Linear Differential Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Siniša Miličić ◽  
Mervan Pašić
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Finite Interval ◽  
Zero Solution ◽  
Two Dimensional ◽  
Matrix Elements ◽  
Differential Systems ◽  
Linear Differential Systems ◽  
Nonautonomous Differential Equations ◽  
Linear Differential

We study the asymptotic behaviour on a finite interval of a class of linear nonautonomous singular differential equations in Banach space by the nonintegrability of the first derivative of its solutions. According to these results, the nonrectifiable attractivity on a finite interval of the zero solution of the two-dimensional linear integrable differential systems with singular matrix-elements is characterized.

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