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Weighted pseudo almost automorphic classical solutions and optimal mild solutions for fractional differential equations and application in fractional reaction-diffusion equations. (English) Zbl 1307.34006

The authors study the existence, uniqueness of weighted pseudo-almost automorphic classical solutions and optimal mild solutions of abstract semilinear fractional differential equations by using analytic semigroup theory, fractional calculus and fixed point theorem. As an application they discuss the weighted pseudo-almost automorphic classical solutions and optimal mild solutions for a fractional reaction-diffusion equation.
Reviewer’s remark: The solution representation in Lemma 3.1 is not verifying the equation (3.2) and the rest of the paper depends on this solution representation.

MSC:

34A08 Fractional ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
47N20 Applications of operator theory to differential and integral equations
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