Research Article
BibTex RIS Cite
Year 2022, , 105 - 112, 01.12.2022
https://doi.org/10.33187/jmsm.1059716

Abstract

References

  • [1] J. Banas, K. Geobel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math., 60, Marcel Dekker, New York and Basel, 1980.
  • [2] M. Mursaleen, Syed M. H. Rizvi, B. Samet, Measures of Noncompactness and their Applications, Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness, 59-125, Springer, Singapore, 2017.
  • [3] S. Baghdad, Existence and stability of solutions for a system of quadratic integral equations in Banach algebras, Ann. Univ. Paedagog. Crac. Stud. Math., 19 (2020), 203-218.
  • [4] S. Baghdad, M. Benchohra, Global existence and stability results for Hadamard-Volterra-Stieltjes integral equation, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 68(2) (2019), 1387-1400.
  • [5] M. Benchohra, M. A. Darwish, On quadratic integral equations of Urysohn type in Fr´echet spaces, Acta Math. Univ. Comenian. (N.S.), 79(1) (2010), 105-110.
  • [6] L. Olszowy, Fixed point theorems in the Fr´echet space C(R+) and functional integral equations on an unbounded interval, Appl. Math. Comput. 218(18) (2012), 9066-9074.
  • [7] K. D. Bierstedt, J. Bonet, Some aspects of the modern theory of Fr´echet spaces, RACSAM. Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat., 97(2) (2003), 159-188.
  • [8] V. Dietmar, Lectures on Fr´echet Spaces, Bergische Universit¨at Wuppertal Sommersemester, 2000.
  • [9] D. Baleanu, A. Jajarmi, H. Mohammadi, S. Rezapour, A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative, Chaos Solitons Fractals, 134 (2020), 109705.
  • [10] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
  • [11] H. Mohammadi, S. Kumar, S. Rezapour; S. Etemad, A theoretical study of the Caputo-Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control, Chaos Solitons Fractals, 144 (2021), 110668.
  • [12] Y.-M. Chu, S. Rashid, F. Jarad, M. A. Noor, H. Kalsoom, More new results on integral inequalities for generalized K -fractional conformable integral operators, Discrete Contin. Dyn. Syst. Ser. S 14(7) (2021), 2119-2135.
  • [13] S. Abbas, M. Benchohra, G. M. N’Gu´er´ekata Advanced Fractional Differential and Integral Equations, Nova Science Publishers, New York, 2015.
  • [14] D. Baleanu, S. Etemad, S. Rezapour, A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions, Bound. Value Probl., 2020(1) (2020), Article number: 64, 16 pages.
  • [15] P. O. Mohammed, T. Abdeljawad, F. Jarad, Y. M. Chu, Existence and uniqueness of uncertain fractional backward difference equations of Riemann-Liouville type, Math. Probl. Eng., 2020 (2020), Article ID: 6598682, 8 pages.
  • [16] J. Bana´s; T. Zaja¸c, A new approach to the theory of functional integral equations of fractional order, J. Math. Anal. Appl., 375(2) (2011), 375-387.
  • [17] S. Abbas, M. Benchohra, J. Henderson, Asymptotic behavior of solutions of nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations, Int. Elect. J. Pure Appl. Math., 4(3) (2012), 195-209.
  • [18] S. Abbas, M. Benchohra, J. J. Nieto, Global attractivity of solutions for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes partial integral equations, Electron. J. Qual. Theory Differ. Equ., 81 (2012), 1-15.
  • [19] S. Samko, A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives (Theorie and Applications), Gordon and Breach Science Publishers, Yverdon, 1993.
  • [20] I. P. Natanson, Theory of Functions of a Real Variable, Ungar, New York, 1960.
  • [21] B. G. Pachpatte, Inequalities for Differential and Integral Equations, William F. Ames, Georgia Institute of Technology, 1998.
  • [22] L. Olszowy, S. Dudek, On generalization of Darbo-Sadovskii type fixed point theorems for iterated mappings in Fr´echet spaces, J. Fixed Point Theory Appl., 20(4) (2018), Article number: 146, 12 pages.
  • [23] J. Daneˇs, Some fixed point theorems, Comment. Math. Univ. Carolinae, 9 (1968), 223-235.
  • [24] F. Wang, H. Zhou, Fixed point theorems in locally convex spaces and a nonlinear integral equation of mixed type, Fixed Point Theory Appl., 2015(1)(2015), Article number: 228228, 11 pages.

Existence Results for Fractional Integral Equations in Frechet Spaces

Year 2022, , 105 - 112, 01.12.2022
https://doi.org/10.33187/jmsm.1059716

Abstract

The objective of this paper is to present results on the existence of solutions for a class of fractional integral equations in Fr\'{e}chet spaces of Banach space-valued functions on the unbounded interval. Our main tool is the technique of measures of noncompactness and fixed points theorems.

References

  • [1] J. Banas, K. Geobel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math., 60, Marcel Dekker, New York and Basel, 1980.
  • [2] M. Mursaleen, Syed M. H. Rizvi, B. Samet, Measures of Noncompactness and their Applications, Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness, 59-125, Springer, Singapore, 2017.
  • [3] S. Baghdad, Existence and stability of solutions for a system of quadratic integral equations in Banach algebras, Ann. Univ. Paedagog. Crac. Stud. Math., 19 (2020), 203-218.
  • [4] S. Baghdad, M. Benchohra, Global existence and stability results for Hadamard-Volterra-Stieltjes integral equation, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 68(2) (2019), 1387-1400.
  • [5] M. Benchohra, M. A. Darwish, On quadratic integral equations of Urysohn type in Fr´echet spaces, Acta Math. Univ. Comenian. (N.S.), 79(1) (2010), 105-110.
  • [6] L. Olszowy, Fixed point theorems in the Fr´echet space C(R+) and functional integral equations on an unbounded interval, Appl. Math. Comput. 218(18) (2012), 9066-9074.
  • [7] K. D. Bierstedt, J. Bonet, Some aspects of the modern theory of Fr´echet spaces, RACSAM. Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat., 97(2) (2003), 159-188.
  • [8] V. Dietmar, Lectures on Fr´echet Spaces, Bergische Universit¨at Wuppertal Sommersemester, 2000.
  • [9] D. Baleanu, A. Jajarmi, H. Mohammadi, S. Rezapour, A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative, Chaos Solitons Fractals, 134 (2020), 109705.
  • [10] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
  • [11] H. Mohammadi, S. Kumar, S. Rezapour; S. Etemad, A theoretical study of the Caputo-Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control, Chaos Solitons Fractals, 144 (2021), 110668.
  • [12] Y.-M. Chu, S. Rashid, F. Jarad, M. A. Noor, H. Kalsoom, More new results on integral inequalities for generalized K -fractional conformable integral operators, Discrete Contin. Dyn. Syst. Ser. S 14(7) (2021), 2119-2135.
  • [13] S. Abbas, M. Benchohra, G. M. N’Gu´er´ekata Advanced Fractional Differential and Integral Equations, Nova Science Publishers, New York, 2015.
  • [14] D. Baleanu, S. Etemad, S. Rezapour, A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions, Bound. Value Probl., 2020(1) (2020), Article number: 64, 16 pages.
  • [15] P. O. Mohammed, T. Abdeljawad, F. Jarad, Y. M. Chu, Existence and uniqueness of uncertain fractional backward difference equations of Riemann-Liouville type, Math. Probl. Eng., 2020 (2020), Article ID: 6598682, 8 pages.
  • [16] J. Bana´s; T. Zaja¸c, A new approach to the theory of functional integral equations of fractional order, J. Math. Anal. Appl., 375(2) (2011), 375-387.
  • [17] S. Abbas, M. Benchohra, J. Henderson, Asymptotic behavior of solutions of nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations, Int. Elect. J. Pure Appl. Math., 4(3) (2012), 195-209.
  • [18] S. Abbas, M. Benchohra, J. J. Nieto, Global attractivity of solutions for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes partial integral equations, Electron. J. Qual. Theory Differ. Equ., 81 (2012), 1-15.
  • [19] S. Samko, A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives (Theorie and Applications), Gordon and Breach Science Publishers, Yverdon, 1993.
  • [20] I. P. Natanson, Theory of Functions of a Real Variable, Ungar, New York, 1960.
  • [21] B. G. Pachpatte, Inequalities for Differential and Integral Equations, William F. Ames, Georgia Institute of Technology, 1998.
  • [22] L. Olszowy, S. Dudek, On generalization of Darbo-Sadovskii type fixed point theorems for iterated mappings in Fr´echet spaces, J. Fixed Point Theory Appl., 20(4) (2018), Article number: 146, 12 pages.
  • [23] J. Daneˇs, Some fixed point theorems, Comment. Math. Univ. Carolinae, 9 (1968), 223-235.
  • [24] F. Wang, H. Zhou, Fixed point theorems in locally convex spaces and a nonlinear integral equation of mixed type, Fixed Point Theory Appl., 2015(1)(2015), Article number: 228228, 11 pages.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Said Baghdad 0000-0001-7165-670X

Publication Date December 1, 2022
Submission Date January 18, 2022
Acceptance Date September 5, 2022
Published in Issue Year 2022

Cite

APA Baghdad, S. (2022). Existence Results for Fractional Integral Equations in Frechet Spaces. Journal of Mathematical Sciences and Modelling, 5(3), 105-112. https://doi.org/10.33187/jmsm.1059716
AMA Baghdad S. Existence Results for Fractional Integral Equations in Frechet Spaces. Journal of Mathematical Sciences and Modelling. December 2022;5(3):105-112. doi:10.33187/jmsm.1059716
Chicago Baghdad, Said. “Existence Results for Fractional Integral Equations in Frechet Spaces”. Journal of Mathematical Sciences and Modelling 5, no. 3 (December 2022): 105-12. https://doi.org/10.33187/jmsm.1059716.
EndNote Baghdad S (December 1, 2022) Existence Results for Fractional Integral Equations in Frechet Spaces. Journal of Mathematical Sciences and Modelling 5 3 105–112.
IEEE S. Baghdad, “Existence Results for Fractional Integral Equations in Frechet Spaces”, Journal of Mathematical Sciences and Modelling, vol. 5, no. 3, pp. 105–112, 2022, doi: 10.33187/jmsm.1059716.
ISNAD Baghdad, Said. “Existence Results for Fractional Integral Equations in Frechet Spaces”. Journal of Mathematical Sciences and Modelling 5/3 (December 2022), 105-112. https://doi.org/10.33187/jmsm.1059716.
JAMA Baghdad S. Existence Results for Fractional Integral Equations in Frechet Spaces. Journal of Mathematical Sciences and Modelling. 2022;5:105–112.
MLA Baghdad, Said. “Existence Results for Fractional Integral Equations in Frechet Spaces”. Journal of Mathematical Sciences and Modelling, vol. 5, no. 3, 2022, pp. 105-12, doi:10.33187/jmsm.1059716.
Vancouver Baghdad S. Existence Results for Fractional Integral Equations in Frechet Spaces. Journal of Mathematical Sciences and Modelling. 2022;5(3):105-12.

29237    Journal of Mathematical Sciences and Modelling 29238

                   29233

Creative Commons License The published articles in JMSM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.