پايداري ميتاگ-لفلر-يرز-اولام معادله ديفرانسيل تابعي تاخيري مرتبه اول

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

ﭼﮑﯿﺪه در اﯾﻦ ﻣﻘﺎﻟﻪ، اﺑﺘﺪا ﺑﻪ ﺗﻌﺮﯾﻒ ﻣﻔﺎﻫﯿﻢ ﭘﺎﯾﺪاري ﻣﯿﺘﺎگ- ﻟﻔﻠﺮ- ﯾﺮز- اوﻻم و ﭘﺎﯾﺪاري ﻣﯿﺘﺎگ- ﻟﻔﻠﺮ- ﯾﺮز- اوﻻم-راﺳﯿﺎس ﻣﯽﭘﺮدازﯾﻢ و ﺳﭙﺲ ﺑﺎ اﺳﺘﻔﺎده از روش ﻧﻘﻄﻪ ﺛﺎﺑﺖ ﺑﺮاي ﻣﻌﺎدﻟﻪي دﯾﻔﺮاﻧﺴﯿﻞ ﺗﺎﺧﯿﺮي ﻣﺮﺗﺒﻪ اول زﯾﺮ، ﭘﺎﯾﺪاري ﻣﯿﺘﺎگ-ﻟﻔﻠﺮ-ﯾﺮز- اوﻻم و ﻣﯿﺘﺎگ- ﻟﻔﻠﺮ- ﯾﺮز-اوﻻم-راﺳﯿﺎس را ﺛﺎﺑﺖ ﻣﯽﮐﻨﯿﻢ:) t, y(t), y(t F  y ﮐﻪ در آن، F ﺗﺎﺑﻊ ﮐﺮاﻧﺪار و ﭘﻄﻮﺳﺘﻪ و 0   ﯾﮏ ﺛﺎﺑﺖ ﺣﻘﯿﻘﯽ ﻣﯽﺑﺎﺷﺪ.

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 condition
I can not transfer formulae here.
Now suppose that the function F satisfy the following condition
I 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