Existence of solutions for a class of nonlinear Volterra singular integral equations

Authors:
Asadollah Aghajani;Józef Bana;Yaghoub Jalilian
Affiliations:
School of Mathematics, Iran University of Science and Technology, Narmark, Tehran 16846 13114, Iran;Department of Mathematics, Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Poland;School of Mathematics, Iran University of Science and Technology, Narmark, Tehran 16846 13114, Iran
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 7
Cited 3

On a class of Urysohn—Stieljes quadratic integral equations and their applications

Journal of Computational and Applied Mathematics - Fixed point theory with applications in nonlinear analysis
On a fractional generalization of the free electron laser equation

Applied Mathematics and Computation
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations

Journal of Computational and Applied Mathematics
Constant-sign solutions for systems of singular integral equations of Hammerstein type

Mathematical and Computer Modelling: An International Journal
Nondecreasing solutions of a quadratic singular Volterra integral equation

Mathematical and Computer Modelling: An International Journal
On solutions of an infinite system of singular integral equations

Mathematical and Computer Modelling: An International Journal

Fractional semilinear differential inclusions

Computers & Mathematics with Applications
The technique of Volterra-Stieltjes integral equations in the application to infinite systems of nonlinear integral equations of fractional orders

Computers & Mathematics with Applications
A generalization of Darbo's theorem with application to the solvability of systems of integral equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.09

Visualization

Abstract

In this paper we prove some results concerning the existence of solutions for a large class of nonlinear Volterra singular integral equations in the space C[0,1] consisting of real functions defined and continuous on the interval [0,1]. The main tool used in the proof is the concept of a measure of noncompactness. We also present some examples of nonlinear singular integral equations of Volterra type to show the efficiency of our results. Moreover, we compare our theory with the approach depending on the use of the theory of Volterra-Stieltjes integral equations. We also show that the results of the paper are applicable in the study of the so-called fractional integral equations which are recently intensively investigated and find numerous applications in describing some real world problems.