Research Article

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

Volume: 5 Number: 3 September 30, 2022
EN

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

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

References

  1. 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. [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. [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. [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. [5] A. Azam, M. Arshad, P. Vetro, On a pair of fuzzy contractive mappings, Math. Comput. Model. 52 (2010) 207-214.
  6. [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. [7] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. 30, (1989) 26-37.
  8. [8] T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65(7) (2006) 1379-1393.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

September 30, 2022

Submission Date

March 18, 2022

Acceptance Date

June 23, 2022

Published in Issue

Year 2022 Volume: 5 Number: 3

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
1.Basil S, Antony S. Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems. RNA. 2022;5(3):279-298. doi:10.53006/rna.1089900
Chicago
Basil, Sushma, and Santhi Antony. 2022. “Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems”. Results in Nonlinear Analysis 5 (3): 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
[1]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, Sept. 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 1, 2022): 279-298. https://doi.org/10.53006/rna.1089900.
JAMA
1.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, Sept. 2022, pp. 279-98, doi:10.53006/rna.1089900.
Vancouver
1.Sushma Basil, Santhi Antony. Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems. RNA. 2022 Sep. 1;5(3):279-98. doi:10.53006/rna.1089900

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