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Zbl 1033.45007
Momani, S. M.; Hadid, S. B.
On the inequalities of integro-differential fractional equations.
(English)
[J] Int. J. Appl. Math. 12, No. 1, 29-37 (2003). ISSN 1311-1728

The authors present integro-differential inequalities results of equations $$u^{(\alpha)}(t)=g(t,u(t))+\int_{t_{0}}^{t}H(t,s(t),u(s))\,ds, \quad t\in J \ \alpha\in \Bbb R, \ \ 0<\alpha\leq 1,$$ with the initial condition $$u^{(\alpha-1)}(t_{0})=u_{0},$$ where $\Bbb R$ is the set of real numbers, $J=[t_{0},t_{0}+a], \ a>0, \ g\in C(J\times \Bbb R^{n},\Bbb R^{n})$ and $H\in C(J\times J\Bbb R^{n},\Bbb R^{n})$. $\Bbb R^{n}$ denotes the real $n$-dimensional Euclidean space.
[Mouffak Benchohra (Sidi Bel Abbes)]
MSC 2000:
*45J05 Integro-ordinary differential equations
26D10 Inequalities involving derivatives, diff. and integral operators
45G10 Nonsingular nonlinear integral equations
26A33 Fractional derivatives and integrals (real functions)

Keywords: integro-differential equations; fractional calculus; integro-differential inequalities

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