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Year 2022, Volume: 5 Issue: 3, 279 - 298, 30.09.2022

Sushma Basil , Santhi Antony

https://doi.org/10.53006/rna.1089900
Cited By: 1

Abstract

References

  • 1] H.M. Abu-Donia, Common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition, Chaos Solitons Fractals. 34(2) (2007) 538-543.
  • [2] J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized F-contraction in complete metric spaces, Fixed Point Theory Appl. 80 (2015) 1-18.
  • [3] T. Allahviranloo, P. Salehi, M. Nejatiyan, Existence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations, Iranian Journal of Fuzzy Systems. 12(2) (2015) 75-86.
  • [4] B. Alqahtani, A. Fulga, F. Jarad and E. Karapınar, Nonlinear F-contractions on b-metric spaces and differential equations in the frame of fractional derivatives with Mittag-Leffler Kernel, Chaos, Solitons and Fractals. 128(C) (2019) 349-354.
  • [5] A. Azam, M. Arshad, P. Vetro, On a pair of fuzzy contractive mappings, Math. Comput. Model. 52 (2010) 207-214.
  • [6] H. Aydi, M.F. Bota, E. Karapınar, S. Moradi, A common fixed point for weak-ϕ-contractions on b-metric spaces, Fixed Point Theory. 13(2) (2012) 337-346.
  • [7] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. 30, (1989) 26-37.
  • [8] T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65(7) (2006) 1379-1393.
  • [9] A. Boutiara, K. Guerbati, M. Benbachir, Caputo-Hadamard fractional differential equation with three-point boundary conditions in Ba- nach spaces, AIMS Mathematics. 5(1) (2019) 259-272.
  • [10] L.B. Ciric, V. Lakshmikantham, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis TMA, 70(12) (2009) 4341-4349.
  • [11] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1(1) (1993) 5-11.
  • [12] M.A. Darwish, On the existence of a fuzzy integral equation of Urysohn-Volterra Type, Discussiones Mathematicae, Differential Inclu- sions, Control and Optimization. 28(1) (2008), 75-82.
  • [13] S. Heilpern, Fuzzy mappings and fixed point theorem, Journal of Mathematical Analysis and Applications, 83 (1981) 566-569.
  • [14] F. Jarad, D. Baleanu and A. Abdeljawad, Caputo-type modification of the Hadamard fractional derivatives, Adv. Differ. Equ. 142 (2012) 1-8.
  • [15] O. Kaleva, Fuzzy differential equations, Fuzzy Sets Syst. 24(3) (1987) 301-317.
  • [16] A.A. Kilbas, H.M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier. 204 (2006).
  • [17] M.A. Kutbi, E. Karapınar, J. Ahmad and A. Azam, Some fixed point results for multivalued mappings in b-metric spaces. 126 (2014) 1-11.
  • [18] B.S. Lee, S.J. Cho, A fixed point theorem for contractive type fuzzy mappings, Fuzzy sets Syst. 61(3) (1994), 309-312.
  • [19] L.V. Nguyena, N.H. Hoc, On nonlinear F-contractive fuzzy mappings, Journal of Intelligent and Fuzzy Systems. 36(6) (2019) 6481-6491.
  • [20] H. Piri, P. Kumam, Wardowski Type Fixed Point Theorems in Complete Metric Spaces, Fixed Point Theory Appl. 45 (2016) 1-12.
  • [21] H. Qawaqneh, M.S. Noorani, W. Shatanawi, H. Aydi, H. Alsamir, Fixed Point Results for Multi-Valued Contractions in b-Metric Spaces and an Application, Mathematics, 7(132) (2019) 1-13.
  • [22] W. Sintunavarat, P. Kumam, Y. J. Cho, Coupled fixed point theorems for nonlinear contractions without mixed monotone property, Fixed Point Theory and Applications. 170 (2012) 1-16.
  • [23] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012) 1-6.
  • [24] D. Wardowski, N. Dung, Fixed points of F-weak contraction on complete metric spaces, Demonstr. Math. XLVII. (2014) 146-155.
  • [25] D. Wardowski, Solving existence problems via F-contractions, Proc. Am. Math. Soc 146(4), (2018) 1585-1598.
  • [26] A. Yacine, B. Nouredine, Boundary value problem for Caputo-Hadamard fractional differential equations, Surveys in Mathematics and its Applications, 12 (2017) 103-115.
  • [27] L.A. Zadeh, Fuzzy sets, Inf. Control. 8 (1965) 338-353.
  • [28] L. Zhu, C.X. Zhu and X.J. Huang, Coupled coincidence and common fixed point theorems for single-valued and fuzzy mappings, Iranian Journal of Fuzzy Systems. 12(1) (2015) 75-87.

Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems

Year 2022, Volume: 5 Issue: 3, 279 - 298, 30.09.2022

Sushma Basil , Santhi Antony

https://doi.org/10.53006/rna.1089900
Cited By: 1

Abstract

In this paper we present fuzzy coupled fixed point results in the turf of complete b-metric spaces via nonlinear F-contraction; in follow we derive some interesting results as byproducts. Eventually, we apply our results in solving fuzzy Volterra integral equations and Caputo-Hadamard type of fractional differential equations.

Keywords

Fuzzy mapping Fuzzy coupled fixed point b-metric space Fuzzy Volterra integral equations Caputo-Hadamard fractional derivative

References

  • 1] H.M. Abu-Donia, Common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition, Chaos Solitons Fractals. 34(2) (2007) 538-543.
  • [2] J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized F-contraction in complete metric spaces, Fixed Point Theory Appl. 80 (2015) 1-18.
  • [3] T. Allahviranloo, P. Salehi, M. Nejatiyan, Existence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations, Iranian Journal of Fuzzy Systems. 12(2) (2015) 75-86.
  • [4] B. Alqahtani, A. Fulga, F. Jarad and E. Karapınar, Nonlinear F-contractions on b-metric spaces and differential equations in the frame of fractional derivatives with Mittag-Leffler Kernel, Chaos, Solitons and Fractals. 128(C) (2019) 349-354.
  • [5] A. Azam, M. Arshad, P. Vetro, On a pair of fuzzy contractive mappings, Math. Comput. Model. 52 (2010) 207-214.
  • [6] H. Aydi, M.F. Bota, E. Karapınar, S. Moradi, A common fixed point for weak-ϕ-contractions on b-metric spaces, Fixed Point Theory. 13(2) (2012) 337-346.
  • [7] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. 30, (1989) 26-37.
  • [8] T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65(7) (2006) 1379-1393.
  • [9] A. Boutiara, K. Guerbati, M. Benbachir, Caputo-Hadamard fractional differential equation with three-point boundary conditions in Ba- nach spaces, AIMS Mathematics. 5(1) (2019) 259-272.
  • [10] L.B. Ciric, V. Lakshmikantham, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis TMA, 70(12) (2009) 4341-4349.
  • [11] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1(1) (1993) 5-11.
  • [12] M.A. Darwish, On the existence of a fuzzy integral equation of Urysohn-Volterra Type, Discussiones Mathematicae, Differential Inclu- sions, Control and Optimization. 28(1) (2008), 75-82.
  • [13] S. Heilpern, Fuzzy mappings and fixed point theorem, Journal of Mathematical Analysis and Applications, 83 (1981) 566-569.
  • [14] F. Jarad, D. Baleanu and A. Abdeljawad, Caputo-type modification of the Hadamard fractional derivatives, Adv. Differ. Equ. 142 (2012) 1-8.
  • [15] O. Kaleva, Fuzzy differential equations, Fuzzy Sets Syst. 24(3) (1987) 301-317.
  • [16] A.A. Kilbas, H.M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier. 204 (2006).
  • [17] M.A. Kutbi, E. Karapınar, J. Ahmad and A. Azam, Some fixed point results for multivalued mappings in b-metric spaces. 126 (2014) 1-11.
  • [18] B.S. Lee, S.J. Cho, A fixed point theorem for contractive type fuzzy mappings, Fuzzy sets Syst. 61(3) (1994), 309-312.
  • [19] L.V. Nguyena, N.H. Hoc, On nonlinear F-contractive fuzzy mappings, Journal of Intelligent and Fuzzy Systems. 36(6) (2019) 6481-6491.
  • [20] H. Piri, P. Kumam, Wardowski Type Fixed Point Theorems in Complete Metric Spaces, Fixed Point Theory Appl. 45 (2016) 1-12.
  • [21] H. Qawaqneh, M.S. Noorani, W. Shatanawi, H. Aydi, H. Alsamir, Fixed Point Results for Multi-Valued Contractions in b-Metric Spaces and an Application, Mathematics, 7(132) (2019) 1-13.
  • [22] W. Sintunavarat, P. Kumam, Y. J. Cho, Coupled fixed point theorems for nonlinear contractions without mixed monotone property, Fixed Point Theory and Applications. 170 (2012) 1-16.
  • [23] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012) 1-6.
  • [24] D. Wardowski, N. Dung, Fixed points of F-weak contraction on complete metric spaces, Demonstr. Math. XLVII. (2014) 146-155.
  • [25] D. Wardowski, Solving existence problems via F-contractions, Proc. Am. Math. Soc 146(4), (2018) 1585-1598.
  • [26] A. Yacine, B. Nouredine, Boundary value problem for Caputo-Hadamard fractional differential equations, Surveys in Mathematics and its Applications, 12 (2017) 103-115.
  • [27] L.A. Zadeh, Fuzzy sets, Inf. Control. 8 (1965) 338-353.
  • [28] L. Zhu, C.X. Zhu and X.J. Huang, Coupled coincidence and common fixed point theorems for single-valued and fuzzy mappings, Iranian Journal of Fuzzy Systems. 12(1) (2015) 75-87.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sushma Basil 0000-0003-3438-8464

Santhi Antony 0000-0001-7715-8533

Publication Date September 30, 2022
Published in Issue Year 2022 Volume: 5 Issue: 3

Cite

APA Basil, S., & Antony, S. (2022). Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems. Results in Nonlinear Analysis, 5(3), 279-298. https://doi.org/10.53006/rna.1089900
AMA Basil S, Antony S. Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems. RNA. September 2022;5(3):279-298. doi:10.53006/rna.1089900
Chicago Basil, Sushma, and Santhi Antony. “Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems”. Results in Nonlinear Analysis 5, no. 3 (September 2022): 279-98. https://doi.org/10.53006/rna.1089900.
EndNote Basil S, Antony S (September 1, 2022) Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems. Results in Nonlinear Analysis 5 3 279–298.
IEEE S. Basil and S. Antony, “Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems”, RNA, vol. 5, no. 3, pp. 279–298, 2022, doi: 10.53006/rna.1089900.
ISNAD Basil, Sushma - Antony, Santhi. “Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems”. Results in Nonlinear Analysis 5/3 (September 2022), 279-298. https://doi.org/10.53006/rna.1089900.
JAMA Basil S, Antony S. Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems. RNA. 2022;5:279–298.
MLA Basil, Sushma and Santhi Antony. “Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems”. Results in Nonlinear Analysis, vol. 5, no. 3, 2022, pp. 279-98, doi:10.53006/rna.1089900.
Vancouver Basil S, Antony S. Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems. RNA. 2022;5(3):279-98.

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