Impulsive differential equations involving general conformable fractional derivative in Banach spaces

In this paper we investigate the following fractional order in time integrodifferential problem $$ \mathbb{D}_{t}^{\alpha}u(t)+Au(t)=f \bigl(t,u(t) \bigr)+ \int _{-\infty}^{t} k(t-s)g \bigl(s,u(s) \bigr)\,ds, \quad t \in \mathbb{R}. $$ D t α u ( t ) + A u ( t ) = f ( t , u ( t ) ) + ∫ − ∞ t k ( t − s ) g ( s , u ( s ) ) d s , t ∈ R . Here, $\mathbb{D}_{t}^{\alpha}$ D t α is the Caputo derivative. We obtain results on the existence and uniqueness of $(\omega ,c)$ ( ω , c ) -periodic mild solutions assuming that −A generates an analytic semigroup on a Banach space X and f, g, and k satisfy suitable conditions. Finally, an interesting example that fits our framework is given.

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$(\omega ,c)$-periodic solutions for a class of fractional integrodifferential equations

Álvarez

Grau

Meriño

2023

Bound Value Probl

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Impulsive differential equations involving general conformable fractional derivative in Banach spaces

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$(\omega ,c)$-periodic solutions for a class of fractional integrodifferential equations

$(\omega ,c)$-periodic solutions for a class of fractional integrodifferential equations

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