Almost automorphic mild solutions to fractional differential equations

By Daniel B. Araya, Carlos Lizama. 2008

223 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/cffa5d53fef8fc03d4437b8643084f81f2b76391

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Citations in the corpus

S‐asymptotically ω‐periodic solutions for semilinear Volterra equations (2010, background): “Related with this subject, we refer the reader to the extensive bibliography in [2, 5, 6, 7, 9, 10, 13, 18, 22, 23, 29, 30].”
On the concept of solution for fractional differential equations with uncertainty (2010, background): “Some recent contributions to the theory of fractional differential equations can be seen in [6–12].”
Square-mean pseudo almost automorphic process and its application to stochastic evolution equations (2011, background): “N’Guérékata for the almost automorphic solutions to the semilinear evolution equations, and see [1] by D.”
Existence of solutions for nonlinear fractional stochastic differential equations (2013, background): “3 ([2]).”
Mild solutions for abstract fractional differential equations (2013, background): “Fractional derivatives in the sense of Riemann–Liouville seem to be more appropriate in studying the qualitative behaviour of abstract fractional differential equations on R, see [28] for an example in this direction.”
On fractional resolvent operator functions (2010, background): “a (2, 1)-ROF is a Sine operator function), which can be applied to research the asymptotic behavior of the solutions to some fractional differential equations and some fractional integro-differential equations, see [ 1 ] and [6] respectively.”
Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators (2020, background): “In 2008, Araya and Lizama in [3] introduce the concept of αorder resolvent operator to prove the existence of almost automorphic mild solutions to a class of semilinear fractional evolution equations.”
Bounded Mild Solutions for Semilinear Integro Differential Equations in Banach Spaces (2010, background): “[3]), and therefore the term limiting equation of (3.”
Bounded mild solutions to fractional integro-differential equations in Banach spaces (2013, background): “Follows the same lines of [4] and [17].”