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Nonlinear functional differential equations of arbitrary orders. (English) Zbl 0934.34055
The initial value problem is considered for the fractional delay differential equation $D^\alpha x(t)= f(t,x(t), D^{\alpha_1} x(t- r),\dots, D^{\alpha_n} x(t- nr)),\tag{1}$
$D^jx(t)= 0,\quad\text{for }t\leq 0,\quad j= 0,1,\dots, n,\tag{2}$ 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:
 34K05 General theory of functional-differential equations
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