Top

Journal of Applied Mathematics and Computing

Published in:

07-12-2015 | Original Research

Existence and stability of Stieltjes quadratic functional integral equations

Authors: Zhi Zhang, JinRong Wang

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2017

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, we investigate existence and generalized Hyers–Ulam–Rassias stability of Stieltjes quadratic functional integral equations. Firstly, we show some basic properties of the composite function of bounded variation. Secondly, we derive the generalized Hyers–Ulam–Rassias stability result after examining the existence and uniqueness results via the theory of measure of noncompactness and a fixed point theorem of Darbo type. Finally, two examples of functional integral equations of fractional order are given to demonstrate the applicability of our results.

previous article Convergence rates of a family of barycentric osculatory rational interpolation

next article On some classes of linear codes over and their covering radii

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

McKee, S., Cuminato, J.A.: Nonlocal diffusion, a Mittag-Leffler function and a two-dimensional Volterra integral equation. J. Math. Anal. Anal. 423, 243–252 (2015)MathSciNetCrossRefMATH

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Science B.V., Amsterdam (2006)MATH

Banaś, J., Zaja̧c, T.: A new approach to the theory of functional integral equations of fractional order. J. Math. Anal. Appl. 375, 375–387 (2011)MathSciNetCrossRef

Aghajani, A., Banaś, J., Jalilian, Y.: Existence of solutions for a class of nonlinear Volterra singular integral equations. Comput. Math. Appl. 62, 1215–1227 (2011)MathSciNetCrossRefMATH

Jankowski, T.: Positive solutions to fractional differential equations involving Stieltjes integral conditions. Appl. Math. Comput. 241, 200–213 (2014)MathSciNetMATH

Abbas, S., Benchohra, M., Rivero, M., Trujillo, J.J.: Existence and stability results for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations. Appl. Math. Comput. 247, 319–328 (2014)MathSciNetMATH

Zhang, X., Liu, L., Wiwatanapataphee, B., Wu, Y.: The eigenvalue for a class of singular \(p\)-Laplacian fractional differential equations involving the Riemann-Stieltjes integral boundary condition. Appl. Math. Comput. 235, 412–422 (2014)MathSciNetMATH

Banaś, J., Rzepka, B.: The technique of Volterra-Stieltjes integral equations in the application to infinite systems of nonlinear integral equations of fractional orders. Comput. Math. Appl. 64, 3108–3116 (2012)MathSciNetCrossRefMATH

Mydlarczyk, W.: The existence problem for a nonlinear Abel equation on the half-line. Nonlinear Anal.: TMA 73, 2022–2026 (2010)MathSciNetCrossRefMATH

10.

Hyers, D.H., Isac, G., Rassias, ThM: Stability of Functional Equations in Several Variables. Birkhäuser, Boston (1998)CrossRefMATH

11.

Pardalos, P.M., Rassias, T.M., Khan A.A.: Nonlinear Analysis and Variational Problems. Springer, Berlin (2010)

12.

Jung, S.M.: Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis. Hadronic Press, PALM HARBOR (2001)MATH

13.

Jung, S.M., Kim, T.S., Lee, K.S.: A fixed point approach to the stability of quadratic functional equation. Bull. Korean Math. Soc. 43, 531–541 (2006)MathSciNetCrossRefMATH

14.

Banaś, J., Goebel, K.: Measures of noncompactness in Banach spaces. Lecture Notes in Pure and Applied Mathematics, vol. 60, (Dekker, New York, 1980)

15.

Garh, M., Rao, A., Kalla, S.I.: Fractional generalization of temperature fields problems in oil strata. Mat. Bilt. 30, 71–84 (2006)MathSciNet

16.

Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)CrossRefMATH

17.

Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Differential Equations. Wiley, New York (1992)MATH

Title: Existence and stability of Stieltjes quadratic functional integral equations
Authors: Zhi Zhang
JinRong Wang
Publication date: 07-12-2015
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2017
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-015-0963-x

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 1-2/2017

Stability by Lyapunov like functions of nonlinear differential equations with non-instantaneous impulses

Fully discrete finite element scheme for nonlocal parabolic problem involving the Dirichlet energy

Convergence rates of a family of barycentric osculatory rational interpolation

Certain types of irregular m-polar fuzzy graphs

Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions

Almost periodic solutions for a competition and cooperation model of two enterprises with time-varying delays and feedback controls

Premium Partner