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Integral equations and initial value problems for nonlinear differential equations of fractional order. (English) Zbl 1169.34302

The paper is concerned with developing existence and uniqueness theory for certain nonlinear integral and integro-differential equations of Volterra and Abel type that arise when the Caputo fractional derivative is used. Following preliminaries, in which the necessary definitions are introduced, the paper presents a series of theorems on existence and uniqueness of solutions under appropriate conditions.

MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
45D05 Volterra integral equations
26A33 Fractional derivatives and integrals
47N20 Applications of operator theory to differential and integral equations
45J05 Integro-ordinary differential equations
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