Mittag-Leffler-Hyers-Ulam Stability For A First Order Delay Functional Differential Equation
Subject Areas : Statisticsleyla Sajedi 1 , Nasrin Eghbali 2
1 - Department of Mathematics, Faculty of Mathematical Sciences University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran
2 - Department of Mathematics, Faculty of Mathematical Sciences University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran
Keywords: پایداری میتاگ-لفلر-هایرز-اولام, پایداری میتاگ-لفلر-هایرز-اولام- راسیاس, معادله دیفرانسیل تاخیری,
Abstract :
In this paper, At first we define Mittag-Leffer-Hyers-Ulam and the Mittag-Leffer-Hyers-Ulam-Rassias stability and then by using the fixed point method, we prove the Mittag-Leffer-Hyers-Ulam and the Mittag-Leffer-Hyers-Ulam-Rassias stability for the first order delay differential equation of the form I can not transfer formulae here. Which F is a bounded continuous function and Τ is a fixed real number.For interval I, suppose that F is a continuous function such that satisfy the following conditionI can not transfer formulae here.Now suppose that the function F satisfy the following conditionI can not transfer formulae here.which Eq is Mittag-Leffler function. In this case there exists a unique function such that we have I can not transfer formulae here.for all... and ....In the other words, the function F is Mittag-Leffler-Hyers-Ulam stable. By changing in the conditions of F we can prove that the delay differential equation is Mittag-Leffler-Hyers-Ulam-Rassias stable.
[1] C. Alsina, R. Ger. On some inequalities and stability results related to the exponential function. J. Inequal. Appl. 2: 373-380(1998)
[2] N. Eghbali, V. Kalvandi, J. M. Rassias. A fixed point approach to the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation. Open Math. 14: 237-246(2016)
[3] D. H. Hyers. On the stability of the linear functional equation. Proc. Nat. Acad. Sci. 27: 222-224(1941)
[4] Th. M. Rassias. On the stability of linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72: 297-300(1978)
[5] S. M. Ulam. A Collection of Mathematical Problems. Interscience Publishers, New York (1968)