Existence and stability of solutions for a system of quadratic integral equations in Banach algebras
Keywords:
quadratic integral equations of fractional orderAbstract
The aim of this paper is to prove the existence and stability of solutions of a system of quadratic integral equations in the Banach algebra of continuous and bounded functions on unbounded rectangle. The main tool used in our considerations is the multiple fixed point theorem which is a consequence of Darbo's fixed point theorem and the technique associated with measures of noncompactness. We also present an illustrative example.
References
Abbas, Saïd et al. "Existence and attractivity results for coupled systems of nonlinear Volterra-Stieltjes multidelay fractional partial integral equations." Abstr. Appl. Anal. (2018): Art. ID 8735614.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Abbas, Saïd, and Mouffak Benchohra, and Juan J. Nieto Roig. "Global attractivity of solutions for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes partial integral equations." Electron. J. Qual. Theory Differ. Equ. (2012): Article no. 81.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Abbas, Saïd et al. "Existence and stability results for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations." Appl. Math. Comput. 247 (2014): 319-328.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Aghajani, Asadollah, and Ali Shole Haghighi. "Existence of solutions for a system of integral equations via measure of noncompactness." Novi Sad J. Math. 44, no. 1 (2014): 59-73.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Aghajani, Asadollah, Reza Allahyari, and Mohammad Mursaleen. "A generalization of Darbo’s theorem with application to the solvability of systems of integral equations." J. Comput. Appl. Math. 260 (2014): 68-77.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Akhmerov, R.R. et al. Measures of Noncompactness and Condensing Operators Vol. 55 of Operator Theory: Advances and Applications. Basel: Birkhäuser Verlag, 1992.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Baghdad, Said, and Mouffak Benchohra. "Global existence and stability results for Hadamard-Volterra-Stieltjes integral equations." Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 68, no. 2 (2019): 1387-1400.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józef. "Existence results for Volterra-Stieltjes quadratic integral equations on an unbounded interval." Math. Scand. 98, no. 1 (2006): 143-160.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józefet et al. "Monotonic solutions of a class of quadratic integral equations of Volterra type." Comput. Math. Appl. 49, no. 5-6 (2005): 943-952.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józef, and Szymon Dudek. "The technique of measures of noncompactness in Banach algebras and its applications to integral equations." Abstr. Appl. Anal. (2013): Art. ID 537897.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józef, and Kazimierz Goebel. Measures of noncompactness in Banach spaces vol. 60 of Lecture Notes in Pure and Applied Mathematics. New York: Marcel Dekker, Inc., 1980.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józef, Millenia Lecko, and Wagdy Gomaa El-Sayed. "Existence theorems for some quadratic integral equations." J. Math. Anal. Appl. 222, no. 1 (1998): 276-285.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józef, and Leszek Olszowy. "On a class of measures of noncompactness in Banach algebras and their application to nonlinear integral equations." Z. Anal. Anwend. 28, no. 4 (2009): 475-498.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józef, and Donal O’Regan. "On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order." J. Math. Anal. Appl. 345, no. 1 (2008): 573-582.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józef, Méndez, and Kishin B. Sadarangani. "On a class of Urysohn-Stieltjes quadratic integral equations and their applications." J. Comput. Appl. Math. 113, no. 1-2 (2000): 35-50.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józef, and Beata Rzepka. "Monotonic solutions of a quadratic integral equation of fractional order." J. Math. Anal. Appl. 332, no. 2 (2007): 1371-1379.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Banaś, Józef, and Kishin B. Sadarangani. "Solvability of Volterra-Stieltjes operator-integral equations and their applications." Comput. Math. Appl. 41, no. 12 (2001): 1535-1544.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Chandrasekhar, Subrahmanyan. Radiative transfer. New York: Dover Publications, 1960.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Corduneanu, Constantin. Integral equations and stability of feedback systems. Vol. 104 of Mathematics in Science and Engineering. New York, London: Academic Press, 1973.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Dhage, Bapurao Chandrabhan. "A coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space with applications." Differ. Equ. Appl. 9, no. 4 (2017): 453-477.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Dhage, Bapurao Chandrabhan and Sidheshwar Sangram Bellale. "Local asymptotic stability for nonlinear quadratic functional integral equations." Electron. J. Qual. Theory Differ. Equ. (2008): Art. no. 10.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Kilbas, Anatoly Aleksandrovich, Hari Mohan Srivastava, and Juan J. Trujillo. Theory and applications of fractional differential equations Vol. 204 of North-Holland Mathematics Studies. Amsterdam: Elsevier Science B.V., 2006.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Lebesgue, Henri Leon. Leçons sur l’intégration et la recherche des fonctions primitives professées au Collège de France. Cambridge Library Collection. Cambridge: Cambridge University Press, 2009. Reprint of the 1904 original.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Isidor Pavlovic Natanson. Theory of functions of a real variable Vol. 85 of North-Holland Mathematics Studies. Berlin: Akademie-Verlag, 1981.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Schwabik, Štefan, Milan Tvrdý and Otto Vejvoda. Differential and integral equations. Dordrecht, Boston, London: D. Reidel Publishing Co., 1979.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Sikorski, Roman. Funkcje rzeczywiste. Warszawa: Państwowe Wydawnictwo Naukowe, 1958. Cited on 209.
##plugins.generic.googleScholarLinks.settings.viewInGS##
