An application of a measure of noncompactness in the study of asymptotic stability

Banaś, Józef; Rzepka, Beata

doi:10.1016/s0893-9659(02)00136-2

Cited by 111 publications

(86 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1.8) under some conditions. The result presented in this work extends substantially Theorem 2 of [3], Theorem 3 of [4], Theorem 2 of [7], and Theorem 3.1 of [9], and improves and modifies Theorem 1 of [7]. A nontrivial example illustrating our result is also given.…”

Section: Introductionsupporting

confidence: 64%

“…The example below reveals that Theorem 3.1 virtually generalizes the corresponding results of [3,4,7,9].…”

Section: S X(a(s)) X(b(s))) − U(t S Y(a(s)) Y(b(s)))supporting

confidence: 57%

“…The theory of integral equations is rapidly developing with the help of tools in functional analysis, topology and fixed-point theory (see, for instance, [1][2][3][4][5][6][7][8][9][10][11] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

“…In 2003, Banaś and Rzepka [3,4] investigated the existence and asymptotic stability of solutions for the nonlinear integral equations…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Solvability and asymptotic stability of a nonlinear functional-integral equation

Liu¹,

Kang²,

Ume³

2011

Applied Mathematics Letters

View full text Add to dashboard Cite

show abstract

Section: Introductionsupporting

confidence: 64%

“…The example below reveals that Theorem 3.1 virtually generalizes the corresponding results of [3,4,7,9].…”

Section: S X(a(s)) X(b(s))) − U(t S Y(a(s)) Y(b(s)))supporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

“…In 2003, Banaś and Rzepka [3,4] investigated the existence and asymptotic stability of solutions for the nonlinear integral equations…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solvability and asymptotic stability of a nonlinear functional-integral equation

Liu¹,

Kang²,

Ume³

2011

Applied Mathematics Letters

View full text Add to dashboard Cite

show abstract

“…Moreover, fractional order differential equations, as functional differential equations [15], are related with causality principles and recently attractivity of solutions of fractional differential equations and fractional functional equations has been intensively investigated (see [8,9,10,11,12,13,17] for more details).…”

Section: Introductionmentioning

confidence: 99%

On the attractivity of solutions for a class of multi-term fractional functional differential equations

Losada

Nieto

Pourhadi

2017

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

Please cite this article as: J. Losada, J.J. Nieto, E. Pourhadi, On the attractivity of solutions for a class of multi-term fractional functional differential equations, Journal of Computational and Applied Mathematics (2015), http://dx. AbstractIn this paper, we present some alternative results concerning with the existence and attractivity dependence of solutions for a class of nonlinear fractional functional differential equations. In our consideration, we apply the well-known Schauder fixed point theorem in conjunction with the technique of measure of noncompactness. Moreover, we provide some examples to illustrate the effectiveness of the obtained results. (2010): 47H10; 34A08. Keywords: Schauder fixed point theorem; attractive solutions; fractional functional differential equations; measure of noncompactness. Mathematics Subject Classification

show abstract

Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

Maleknejad

Mollapourasl

Mirzaei

2013

Numerical Methods Partial

View full text Add to dashboard Cite

In this article, we consider a class of nonlinear functional integral equations which has rather general form and contains a lot of particular cases such as functional equations and nonlinear integral equations of Volterra type. We use a combination of a fixed point method and cubic semiorthogonal B‐spline scaling functions to solve the integral equation numerically. We provide an error analysis for the method which shows that the approximate solution converges to the exact solution. Some numerical results for several test problems are given to confirm the accuracy and the ease of implementation of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 699–722, 2014

show abstract

An application of a measure of noncompactness in the study of asymptotic stability

Cited by 111 publications

References 2 publications

Solvability and asymptotic stability of a nonlinear functional-integral equation

Solvability and asymptotic stability of a nonlinear functional-integral equation

On the attractivity of solutions for a class of multi-term fractional functional differential equations

Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

Contact Info

Product

Resources

About