Japundzic, MilosRajter-Ciric, Danijela2022-09-262022-09-262017-11-27Japundzic, M., & Rajter-Ciric, D. (2017). Generalized uniformly continuous solution operators and inhomogeneous fractional evolution equations with variable coefficients. <i>Electronic Journal of Differential Equations, 2017</i>(293), pp. 1-24.1072-6691https://hdl.handle.net/10877/16165We consider Cauchy problem for inhomogeneous fractional evolution equations with Caputo fractional derivatives of order 0 < α < 1 and variable coefficients depending on x. In order to solve this problem we introduce generalized uniformly continuous solution operators and use them to obtain the unique solution on a certain Colombeau space. In our solving procedure, instead of the original problem we solve a certain approximate problem, but therefore we also prove that the solutions of these two problems are associated. At the end, we illustrate the applications of the developed theory by giving some appropriate examples.Text24 pages1 file (.pdf)enAttribution 4.0 InternationalFractional evolution equationFractional Duhamel principleGeneralized Colombeau solution operatorFractional derivativeMittag-Leffler type functionArticle