Existence of anti-periodic mild solutions for a class of semilinear fractional differential equations. (English) Zbl 1248.35218
Summary: This work is concerned with the existence of anti-periodic mild solutions for a class of semilinear fractional differential equations
\[
D^\alpha_t x(t)= Ax(t)+ D^{\alpha-1}_t F(t,x(t)),\quad t\in\mathbb{R},
\]
where \(1< \alpha< 2\), \(A\) is a linear densely defined operator of sectorial type of \(\omega< 0\) on a complex Banach space \(X\) and \(F\) is an appropriate function defined on phase space, the fractional derivative is understood in the Riemann-Liouville sense. The results obtained are utilized to study the existence of anti-periodic mild solutions to a fractional relaxation-oscillation equation.
MSC:
| 35R11 | Fractional partial differential equations |
| 35D30 | Weak solutions to PDEs |
| 32K05 | Banach analytic manifolds and spaces |
Keywords:
anti-periodic mild solutions; semilinear fractional differential equations; solution operator; fractional integralReferences:
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