$(\omega ,c)$-periodic solutions for a class of fractional integrodifferential equations
$(\omega ,c)$-periodic solutions for a class of fractional integrodifferential equations
Abstract In this paper we investigate the following fractional order in time integrodifferential problem $$ \mathbb{D}_{t}^{\alpha}u(t)+Au(t)=f \bigl(t,u(t) \bigr)+ \int _{-\infty}^{t} k(t-s)g \bigl(s,u(s) \bigr)\,ds, \quad t \in \mathbb{R}. $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>t</mml:mi> <mml:mi>α</mml:mi> </mml:msubsup> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>A</mml:mi> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> …