Weighted pseudo almost automorphic solution of an integro-differential equation, with weighted Stepanov-like pseudo almost automorphic forcing term. (English) Zbl 1285.45005

Mishra, Indira; Bahuguna, D.

Appl. Math. Comput. 219, No. 10, 5345-5355 (2013).

The authors prove the existence and uniqueness of weighted pseudo almost automorphic solutions to an abstract integro-differential equation. The paper generalizes a recent work by S. Abbas [Comput. Math. Appl. 62, No. 5, 2259–2272 (2011; Zbl 1231.45015)]. An example of an integro-partial differential equation is included.

Reviewer: Sergiu Aizicovici (Athens/Ohio)

MSC:

45N05	Abstract integral equations, integral equations in abstract spaces
45J05	Integro-ordinary differential equations
45K05	Integro-partial differential equations

Keywords:

almost automorphic function; mild solution; evolution equation; weighted pseudo almost automorphic function; \(S^p\)-weighted pseudo almost automorphic function; fractional powers of operators; abstract integro-differential equation; integro-partial differential equation