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Zbl 0934.34055
El-Sayed, Ahmed M.A.
Nonlinear functional differential equations of arbitrary orders.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 33, No.2, 181-186 (1998). ISSN 0362-546X

The initial value problem is considered for the fractional delay differential equation $$D^\alpha x(t)= f(t,x(t), D^{\alpha_1} x(t- r),\dots, D^{\alpha_n} x(t- nr)),\tag 1$$ $$D^jx(t)= 0,\quad\text{for }t\le 0,\quad j= 0,1,\dots, n,\tag 2$$ with $\alpha\in (n,n+1]$, $\alpha_k\in (k- 1,k]$, $k= 1,\dots, n$. A sufficient condition for the existence of at least one (nondecreasing) solution to (1), (2) is established.
MSC 2000:
*34K05 General theory of functional-differential equations

Keywords: nondecreasing solution; initial value problem; fractional delay differential equation; existence

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