Generalized uniformly continuous solution operators and inhomogeneous fractional evolution equations with variable coefficients
Date
2017-11-27
Authors
Japundzic, Milos
Rajter-Ciric, Danijela
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Fractional evolution equation, Fractional Duhamel principle, Generalized Colombeau solution operator, Fractional derivative, Mittag-Leffler type function
Citation
Japundzic, 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.
Rights
Attribution 4.0 International