Nonlinear functional differential equations of arbitrary orders. (English) Zbl 0934.34055

El-Sayed, Ahmed M. A.

Nonlinear Anal., Theory Methods Appl. 33, No. 2, 181-186 (1998).

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.

Reviewer: R.G.Koplatadze (Tbilisi)

MSC:

34K05

General theory of functional-differential equations

Keywords:

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

References:

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