Existence and Attractivity for Fractional Evolution Equations

Abstract

We study the existence and attractivity of solutions for fractional evolution equations with Riemann-Liouville fractional derivative. We establish sufficient conditions for the global attractivity of mild solutions for the Cauchy problems in the case that semigroup is compact.

Existence of solutions for semilinear fractional integro-differential equations with nonlocal conditions

“…Wang and Zhou [41] researched sufficient conditions for the complete controllability of fractional evolution systems with the help of the fractional calculus, properties of characteristic solution operators and fixed point technique. Utilizing the theory of fractional calculus and Schauder fixed point theorem, Zhou et al [46] derived sufficient conditions for the existence and attractivity of solutions for fractional evolution equations with Riemann-Liouville fractional derivative. For more relative works, see [5,15,22,25,35,39].…”

Existence results of solution for fractional Sturm–Liouville inclusion involving composition with multi-maps

“…where α ∈ [0, 1), R D α and I 1−α are respectively Riemann-Liouville derivative and integral of orders α and 1 − α. After that, he in [22] has improved the previous problem up to more general by the next Riemann-Liouville fractional differential evolution equations:…”

Analysis of fractional boundary value problem with non local flux multi-point conditions on a Caputo fractional differential equation

“…These equations capture non local relations in space and time with memory essentials. Due to extensive applications of FDEs in engineering and science, research in this area has grown significantly all around the world., for instance, see [18], [11], [15] and the references cited therein. Recently, much interest has been created in establishing the existence of solutions for various types of boundary value problem of fractional order with nonlocal multi-point boundary conditions.…”