Existence and uniqueness of solutions for differential equations with causal operators

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Mazandaran, Babolsar, Iran

2 Technical and Vocational University (TVU), Tehran, Iran

Abstract

In this paper, we consider the existence and uniqueness of a solution for interval-valued differential functions with a causal operator.

Keywords

[1] Z. Drici, F.A. Mcrae, and J.V. Devi, Set differential equations with causal operators, Math. Prob. Engin. 2005 (2005), no. 2, 185–194.
[2] N. Khorrami, A. Salimi Shamloo, and B. Parsa Moghaddam, Numerical solution of interval Volterra-Fredholm-Hammerstein integral equations via interval Legendre wavelets method, Int. J. Ind. Math. 13 (2021), no. 1, 15–28.
[3] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, Vol. I. Ordinary Differential Equations, Academic Press, New York, 1969.
[4] T. Lou, G. Ye, D. Zhao, and W. Liu, Iq-calculus and Iq-Hermite-Hadamard inequalities for interval-valued functions, Adv. Differ. Equ. 446 (2020), 1–22.
[5] N.D. Phu, T.V. An, N.V. Hao, and N. Hien, Interval-valued functional differential equations under dissipative conditions, Adv. Differ. Equ. 198, (2014), 1–19.
[6] P. Roy and G. Panda, Expansion of generalized Hukuhara differentiable interval valued function, New Math. Natural Comput. 15 (2019), no. 3, 553–570.
[7] L. Stefanini and B. Bede, Some notes on generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Working Paper 1208, University of Urbino, 2012. Available online at the RePEc repository, http://ideas.repec.org/f/pst233.html
[8] L. Stefanini and B. Bede, Generalized Hukuhara differentiability of interval- valued functions and interval differential equations, Nonlinear Anal. 71 (2009), 1311–1328.
[9] J. Tao and Z. Zang, Properties of interval-valued function space under the gH-difference and their application to semi-linear interval differential equations, Adv. Differ. Equ. 45 (2016), 1–28.

Articles in Press, Corrected Proof
Available Online from 29 May 2025
  • Receive Date: 19 June 2024
  • Accept Date: 20 October 2024