Qualitative behaviour of solutions of hybrid fractional integral equation with linear perturbation of second kind in Banach space

Downloads

DOI:

https://doi.org/10.26637/MJM0603/0008

Abstract

In this paper, we present existence and qualitative behaviour of solution of hybrid fractional integral equation with linear perturbation of second kind by applying measure of noncompactness in Banach space. We established our result in the Banach space of real-valued functions defined, continuous and bounded in the right hand real axis.

Keywords:

Hybrid fractional integral equation, measure of noncompactness, attractivity of solution

Mathematics Subject Classification:

Mathematics
  • Pages: 506-513
  • Date Published: 01-07-2018
  • Vol. 6 No. 03 (2018): Malaya Journal of Matematik (MJM)

Agarwal R.P., ORegan D., Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 2001.

Apell J., Measure of noncompactness, condensing operator and fixed points: an applications-oriented survey, Fixed point theory, 2005; 6: 157-229.

Balachandran K., Julie D., Asymptotic stability of solutions of nonlinear integral equations, Nonlinear Funct. Anal. Appl., 2008; 2: 313-322.

Banas J., Cabrera I.J, On existence and asymptotic behaviour of solutions of a functional integral equation, Nonlinear Anal., 2007; 66: 2246-2254.

Banas J, Sadarangani K., Solutions of some functional integral equations in Banach algebra, Math. Comput. Modell., $2003 ; 38: 245-250$.

Banas J., Rzepka B. , An application of a measure of noncompactness in the study of asymptotic stability, App Math letters, $2003 ; 16 ; 1-6$.

Banas J., Goebel K., Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, Basel, 1980.

Bloom F., Closed Asymptotic bound for Solution to a System of Damped Integro-differential Equations of Electromagnetic Theory, J. Math. Ana. Appl.,1980; 73;524542.

Burton T.A., Volterra Integral and Differential Equations, Academic Press, New York, 1983.

Darwish M.A., On solvability of some quadratic functional integral equation in Banach algebra, Commun. Appl. Anal., 2007; 11;441-450.

Dhage B.C., Dhage S.B. and Graef J.B., Local attractivity and stability analysis of a nonlinear quadratic fractional integral equation, Applicable Analysis, 2016; 95(9): 19892003.

Dhage B.C., Attractivity and positivity results for nonlinear functional integral equations via measure of noncompactness, Diff. Equations and App., 2010; 12(2): 299_ 318.

Dhage B.C., Global attractivity result for nonlinear functional integral equation via Krasnoleskii type fixed point theorem, Nonlinear Analysis, 2009; 70: 2485-2493.

Dhage B.C., Asymptotic stability of nonlinear functional integral equations via measure of noncompactness, Comm. App. Nonlinear Ana., 2008; 15(2): 89-101.

Dhage B.C., A fixed point theorem in Banach algebras with applications to functional integral equations, Kyungpook Math. J., 2006; 44: 145-155.

Dhage B.C., Lakshmikantham V., On global existence and attractivity results for nonlinear functional integral equations, Nonlinear Anal., 2010; 72: 2219-2227.

Hu X., Yan J., The global attractivity and asymptotic stability of solution of a nonlinear integral equation, J. Math. Anal. Appl., 2006; 321: 147-156.

Jiang S., Rokhlin V., Second Kind Integral Equation for the Classical Potential Theory on open Surface II, J. Compu. Phy.,2004; 195; 1-16, .

Smart D.R., Fixed Point Theorems, Cambridge Univ. Press, Cambridge, 1980.

Voitovich N., Reshnyak O., Solutions of Nonlinear Integral Equation of Synthesis of the Linear Antenna Arrays, BSUAE J. Appl. Electron., 1999; 2; 49-52.

Metrics

Metrics Loading ...

Published

01-07-2018

How to Cite

Kavita Sakure, and Samir Dashputre. “Qualitative Behaviour of Solutions of Hybrid Fractional Integral Equation With Linear Perturbation of Second Kind in Banach Space”. Malaya Journal of Matematik, vol. 6, no. 03, July 2018, pp. 506-13, doi:10.26637/MJM0603/0008.