@article{DiethelmSiegmundTuan, author = {Diethelm, Kai and Siegmund, Stefan and Tuan, Hoang The}, title = {Asymptotic behavior of solutions of linear multi-order fractional differential systems}, series = {Fractional Calculus and Applied Analysis}, volume = {20}, journal = {Fractional Calculus and Applied Analysis}, doi = {10.1515/fca-2017-0062}, pages = {1165 -- 1195}, abstract = {In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of linear multi-order fractional differential equation systems.}, language = {en} } @article{DiethelmKitzingPicardetal., author = {Diethelm, Kai and Kitzing, Konrad and Picard, Rainer and Siegmund, Stefan and Trostorff, Sascha and Waurick, Marcus}, title = {A Hilbert Space Approach to Fractional Differential Equations}, series = {Journal of Dynamics and Differential Equations}, volume = {34}, journal = {Journal of Dynamics and Differential Equations}, doi = {10.1007/s10884-020-09932-6}, pages = {481 -- 504}, abstract = {We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on R, we define fractional operators by means of a functional calculus using the Fourier transform. Main tools are extrapolation- and interpolation spaces. Main results are the existence and uniqueness of solutions and the causality of solution operators for non-linear fractional differential equations.}, language = {en} }