Abstract
In this paper, explicit solutions of a class of generalized space-time fractional Cauchy problems with time-variable coefficients are given. The representation of a solution involves kernels given by convergent infinite series of fractional integro-differential operators, which can be extensively and efficiently applied for analytic and computational goals. Time-fractional operators of complex orders with respect to a given function are used. Further, we study inverse Cauchy problems of finding time dependent coefficients for fractional wave and heat type equations, which involve the explicit representation of the solution of the direct Cauchy problem and a recent method to recover variable co-efficients for the considered inverse problems. Concrete examples and particular cases of the obtained results are discussed
| Original language | English |
|---|---|
| Pages (from-to) | 305-339 |
| Number of pages | 35 |
| Journal | Advances in Differential Equations |
| Volume | 26 |
| Issue number | 7-8 |
| Publication status | Published - Jul 2021 |
Funding
Acknowledgment. This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09058317). Both authors were supported by the Nazarbayev University Program 091019CRP2120. Joel E. Restrepo thanks to Colciencias and This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09058317). Both authors were supported by the Nazarbayev University Program 091019CRP2120. Joel E. Restrepo thanks to Colciencias and Universidad de Antioquia (Convocatoria 848 - Programa de estancias post-doctorales 2019) for their support. The authors would like to express their sincere gratitude to Prof. Armen Jerbashian for his valuable suggestions and discussions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics