Mittag-Leffler-Hyers-Ulam Stability For A First Order Delay Functional Differential Equation

Subject Areas : Statistics

leyla Sajedi ¹ (Department of Mathematics, Faculty of Mathematical Sciences University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran)
Nasrin Eghbali ² (Department of Mathematics, Faculty of Mathematical Sciences University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran)

Received: 2020-05-31 Accepted : 2021-05-27 Published : 2021-11-22

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.

References:

 

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