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Zbl 1175.34080
Belarbi, Abdelkader; Benchohra, Mouffak; Ouahab, Abdelghani
Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces.
(English)
[J] Appl. Anal. 85, No. 12, 1459-1470 (2006). ISSN 0003-6811; ISSN 1563-504X/e

The paper is concerned with the existence and uniqueness of a solution to an initial value problem for functional differential equations with unbounded delay and fractional order of the form: $$D^{\alpha}[y(t)-g(t,y_t)]=f(t,y_t),\quad 0<\alpha <1,\ t \in[0,\infty ),\ y(t)= \varphi (t),\ t\in (-\infty , 0].$$ The main tool of proving the results is the nonlinear Leray-Schauder type alternative for contractive mappings in Fréchet spaces due to {\it M. Frigon} and {\it A. Granas} [Ann. Sci. Math. Qué. 22, No.~2, 161--168 (1998; Zbl 1100.47514)].
[Jozef Myjak (L'Aquila)]
MSC 2000:
*34K05 General theory of functional-differential equations
26A42 Ordinary integrals of functions of one real variable
26A33 Fractional derivatives and integrals (real functions)
47N20 Appl. of operator theory to differential and integral equations

Keywords: fractional functional differential equations; fractional order integrals; infinite delay; nonlinear Leray-Schauder alternative

Citations: Zbl 1100.47514

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