Integro-Differential Equations of Fractional Order
Copyright policy )Integro-Differential Equations of Fractional Order
For a Cauchy type problem for a two-dimensional integro-differential equation of fractional order the global unique existence of a solution is proved if the nonlinearity satisfies a global Lipschitz condition with a sufficiently small Lipschitz constant. The existence is proved also under a sublinear growth condition of the nonlinearity and also under a more restrictive condition. The proofs are straightforward applications of the fixed point theorems of Banach and Leray-Schauder, using a known Gronwall lemma for the considered problems.
- Université de Saida Dr.Moulay Tahar Algeria
- Université Djillali Liabes Algeria
- SIDI Italy
- University of Tennessee at Chattanooga United States
Other nonlinear integral equations, Cauchy problem, Schauder's fixed point theorem, Gronwall lemma, function of two variables, Banach's contraction principle, nonlinear alternative of Leray-Schauder type, Caputo fractional-order derivative, left-sided mixed Riemann-Liouville integral of fractional order, Integro-ordinary differential equations, Fixed-point theorems, Fractional derivatives and integrals, integro-differential equation of fractional order, existence result
Other nonlinear integral equations, Cauchy problem, Schauder's fixed point theorem, Gronwall lemma, function of two variables, Banach's contraction principle, nonlinear alternative of Leray-Schauder type, Caputo fractional-order derivative, left-sided mixed Riemann-Liouville integral of fractional order, Integro-ordinary differential equations, Fixed-point theorems, Fractional derivatives and integrals, integro-differential equation of fractional order, existence result
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