Rothe's method for solving multi-term Caputo-Katugampola fractional delay integral diffusion equations

作者：Du, Jinsheng; Lu, Cuizhi; Jiang, Yirong^*

来源：MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45(12): 7426-7442.

DOI：10.1002/mma.8250

• multi-term Caputo-Katugampola fractional delay integral diffusion equations
• Rothe's method
• strong solution

This paper discusses a class of multi-term Caputo-Katugampola fractional delay integral diffusion equations (MCKFIDEs, for short) in Hilbert spaces. A iterative scheme in interval [-tau,T similar to],0<T similar to <= T corresponding to the MCKFIDE is introduced by using a temporally semi-discrete method based on the backward Euler difference scheme, i.e., Rothe's method. First, we apply the iterative scheme and the m-accretivity of operator A to establish existence, uniqueness, and a priori estimate for strong solutions to an approximate problem. Based on this result, we obtain existence, regularity of the strong solution for MCKFIDEs on interval [-tau,T] or the maximum interval separators=-tau,tmax,0<tmax <= T. Then, we also prove that the strong solution is unique if and only if the delay boundary condition is unique on [-tau,0]. Finally, two examples are given to illustrate the main results.

• 单位
  桂林理工大学