On some characterizations of the solutions of a hybrid nonlinear functional integral inclusion and applications

Volume 28, Issue 1, pp 21--36 http://dx.doi.org/10.22436/jmcs.028.01.03

Publication Date: April 16, 2022 Submission Date: November 28, 2021 Revision Date: February 09, 2022 Accteptance Date: March 10, 2022

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Authors

Sh. M. Al-Issa - Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon. - Faculty of Arts and Sciences, Department of Mathematics, The International University of Beirut, Beirut, Lebanon. A. M. A. El-Sayed - Faculty of Science, Department of Mathematics, Alexandria University, Alexandria, Egypt. Y. M. Y. Omar - Faculty of Science, Department of Mathematics, Omar Al-Mukhtar University, Tripoli, Libya.

Abstract

Here, we prove two existence theorems for the solutions a hybrid nonlinear functional integral inclusion and study some properties and applications of these two theorems. A Chandrasekhar quadratic integral inclusion and a nonlinear cubic Chandrasekhar functional integral equation are studied as an application. The continuous dependence of the solutions on some functions is proved. \begin{keyword}Hybrid integral equations \sep Urysohn-Stieltjes type integral inclusion \sep Chandrasekhar quadratic integral inclusion \sep cubic Chandrasekhar integral equation. \MSC{26A33 \sep 34A60 \sep 45G05

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Keywords

• Hybrid integral equations
• Urysohn-Stieltjes type integral inclusion
• Chandrasekhar quadratic integral inclusion
• cubic Chandrasekhar integral equation

MSC

•  26A33
•  34A60
•  45G05

References

• [1] J. Appell, J. Banas, N. Merentes, Bounded variation and around, De Gruyter, Berlin (2014)
  • View Article
  • MathSciNet
  • MATH


• [2] I. K. Argyros, Quadratic equations and applications to Chandrasekhar's and related equations, Bull. Austral. Math. Soc., 32 (1985), 275--292
  • View Article
  • MathSciNet


• [3] J.-P. Aubin A. Cellina, Differential Inclusion, Springer-Verlag, Berlin (1984)
  • View Article
  • MathSciNet


• [4] J. Banas, Some properties of Urysohn-Stieltjes integral operators, Internat. J. Math. Math. Sci., 21 (1998), 79--88
  • View Article
  • MathSciNet


• [5] J. Banas, M. Lecko, W. G. El-Sayed, Existence theorems for some quadratic integral equations, J. Math. Anal. Appl., 222 (1998), 276--285
  • View Article
  • MathSciNet


• [6] J. Banas, D. O'Regan, Volterra-Stieltjes integral operators, Math. Comput. Modelling, 41 (2005), 335--344
  • View Article
  • MathSciNet


• [7] J. Banas, J. R. Rodriguez, K. Sadarangani, On a class of Urysohn-Stieltjes quadratic integral equations and their applications, J. Comput. Appl. Math., 113 (2000), 35--50
  • View Article
  • MathSciNet


• [8] J. Banas, K. Sadarangani, Solvability of Volterra-Stieltjes operator-integral equations and their applications, Comput. Math. Appl., 41 (2001), 1535--1544
  • View Article
  • MathSciNet


• [9] I. W. Busbridge, On Solutions of Chandrasekhar's Integral Equation, Trans. Amer. Math. Soc., 105 (1962), 112--117
  • View Article
  • MathSciNet


• [10] B. Cahlon, M. Eskin, Existence theorems for an integral equation of the Chandrasekhar $H$-equation with perturbation, J. Math. Anal. Appl., 83 (1981), 159--171
  • View Article
  • MathSciNet


• [11] J. Callero, A. B. Mingarelli, K. Sadrangani, Existence of solutions of an integral equation of Chandrasekhar type in the theory of radiative transfer, J. Differential Equations, 2006 (2006), 11 pages
  • View Article
  • MathSciNet


• [12] A. Cellina, S. Solimini, Continuous extensions of selections, Bull. Polish Acad. Sci. Math., 35 (1989), 573--581
  • View Article
  • MathSciNet
  • Google Scholar


• [13] C. Derbazi, H. Hammouche, M. Benchohra, Y. Zhou, Fractional hybrid differential equations with three-point boundary hybrid conditions, Adv. Difference Equ., 2019 (2019), 11 pages
  • View Article
  • MathSciNet


• [14] B. C. Dhage, Hybrid fixed point theory in partially ordered normed linear spaces and applications to fractional integral equations, Differ. Equ. Appl., 5 (2013), 155--184
  • View Article
  • MathSciNet


• [15] B. C. Dhage, V. Lakshmikantham, Basic results on hybrid differential equations, Nonlinear Anal. Hybrid Syst., 4 (2010), 414--424
  • View Article
  • MathSciNet


• [16] A. M. A. El-Sayed, M. M. A. Al-Fadel, On a coupled system of Urysohn$-$Stieltjes integral equations in reflexive Banach space, Differ. Uravn. Protsessy Upr., 2018 (2018), 142--153
  • View Article
  • MathSciNet


• [17] A. M. A. El-Sayed, M. M. A. Al-Fadel, Solvability of Urysohn-Stieltjes integral equation in reflexive Banach space, Electron. J. Math. Anal. Appl., 6 (2018), 44--50
  • View Article
  • MathSciNet


• [18] A. M. A. El-Sayed, M. M. A. Al-Fadel, Weak solutions of a coupled system of urysohn-stieltjes functional (delayed) integral equations, Complexity, 2018 (2018), 6 pages
  • View Article
  • Google Scholar


• [19] A. M. A. El-Sayed, S. M. Al-Issa, Monotonic solutions for a quadratic integral equation of fractional order, AIMS Mathematics, 4 (2019), 821--830
  • View Article
  • Google Scholar


• [20] A. M. A. El-Sayed, S. M. Al-Issa, On the existence of solutions of a set-valued functional integral equation of Volterra$-$Stieltjes type and some applications, Adv. Difference Equ., 2020 (2020), 16 pages
  • View Article
  • MathSciNet


• [21] A. M. A. El-Sayed, S. M. Al-Issa, On a set-valued functional integral equation of Volterra-Stiltjes type, J. Math. Computer Sci., 21 (2020), 273--285
  • View Article
  • Google Scholar


• [22] A. M. A. El-Sayed, S. M. Al-Issa, On set-valued functional integral equations of Hammerstein-Stieltjes type: existence of solutions, continuous dependence, and applications, Methods Funct. Anal. Topology, 27 (2021), 157--172
  • View Article
  • MathSciNet


• [23] A. M. A. El-Sayed, S. M. Al-Issa, M. H. Hijazi, Existence results for a functional integro-differential inclusions with Riemann-Stieltjes integral or infinite-point boundary conditions, Surv. Math. Appl., 16 (2021), 301--325
  • View Article
  • MathSciNet


• [24] A. El-Sayed, S. Al-Issa, Y. Omar, On Chandrasekhar functional integral inclusion and Chandrasekhar quadratic integral equation via a nonlinear Urysohn–Stieltjes functional integral inclusion, Adv Difference Equ., 2021 (2021), 17 pages
  • View Article
  • MathSciNet


• [25] A. M. A. El-Sayed, H. H. Hashem, S. M. Al-Issa, An Implicit Hybrid delay functional integral equation: Existence of integrable solutions and continuous dependence, Mathematics, 9 (2021), 16 pages
  • View Article
  • Google Scholar


• [26] A. M. A. El-Sayed, A.-G. Ibrahim, Multivalued fractional differential equations, Appl. Math. Comput., 68 (1995), 15--25
  • View Article
  • MathSciNet
  • Google Scholar


• [27] A. M. A. El-Sayed, A.-G. Ibrahim, Set-valued integral equations of fractional-orders, Appl. Math. Comput., 118 (2001), 113--121
  • View Article
  • MathSciNet
  • MATH


• [28] A. M. A. El-Sayed, Y. M. Y. Omar, P-Chandrasekhar integral equation, Adv. Math. Sci. J., 9 (2020), 10305--10311
  • View Article


• [29] A. M. A. El-Sayed, Y. M. Y. Omar, Chandrasekhar quadratic and cubic integral equations via Volterra$-$Stieltjes quadratic integral equation, Demonstr. Math., 54 (2021), 25--36
  • View Article
  • MathSciNet


• [30] K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambirdge Universty Press, Cambridge (1990)
  • View Article
  • MathSciNet
  • MATH


• [31] H. H. G. Hashem, A. A. Alhejelan, Solvability of Chandrasekhar's quadratic integral equations in Banach algebra, Appl. Math., 8 (2017), 846--856
  • View Article
  • Google Scholar


• [32] M. A. Hernandez-Veron, E. Martinez, S. Singh, On the Chandrasekhar integral equation, Comput. Math. Methods, 2021 (2021), 14 pages
  • View Article
  • MathSciNet


• [33] A. N. Kolmogorov, S. V. Fomin, Introductory Real Analysis, Dover Publications, New York (1975)
  • View Article
  • MathSciNet


• [34] H. A. H. Salem, On the quadratic integral equations and their applications, Comput. Math. Appl., 62 (2011), 2931--2943
  • View Article
  • MathSciNet


• [35] Y. Zhao, S. R. Sun, Z. L. Han, Q. P. Li, Theory of fractional hybrid differential equations, Comput. Math. Appl., 62 (2011), 1312--1324
  • View Article
  • MathSciNet
  • Google Scholar