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Integral solutions of fractional evolution equations with nondense domain. (English) Zbl 1377.34010

Summary: In this article, we study the existence of integral solutions for two classes of fractional order evolution equations with nondensely defined linear operators. First, we consider the nonhomogeneous fractional order evolution equation and obtain its integral solution by Laplace transform and probability density function. Subsequently, based on the form of integral solution for nonhomogeneous fractional order evolution equation, we investigate the existence of integral solution for nonlinear fractional order evolution equation by noncompact measure method.

MSC:

34A08 Fractional ordinary differential equations
47J35 Nonlinear evolution equations
47N20 Applications of operator theory to differential and integral equations
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