Translator Disclaimer
Winter 2020 On the existence, uniqueness and stability results for time-fractional parabolic integrodifferential equations
Shantiram Mahata, Rajen Kumar Sinha
J. Integral Equations Applications 32(4): 457-477 (Winter 2020). DOI: 10.1216/jie.2020.32.457

Abstract

We study the time-fractional parabolic integrodifferential equations with the Caputo fractional time derivative of order α(0,1) in a bounded convex polygonal domain in d. We prove the existence and uniqueness of the solution using the eigenfunction expansion and establish a priori bounds for the solution under various regularity assumptions on the initial data and the source function. Our study includes the initial data in the spaces 2(Ω), H01(Ω) and L2(Ω) while the source function belongs to the class of Hölder continuous and bounded functions. It is shown that the solution of the corresponding homogeneous problem is infinitely differentiable with respect to time t when the initial function is an element of L2(Ω). Finally, we derive a general stability results for the solution of the homogeneous problem.

Citation

Download Citation

Shantiram Mahata. Rajen Kumar Sinha. "On the existence, uniqueness and stability results for time-fractional parabolic integrodifferential equations." J. Integral Equations Applications 32 (4) 457 - 477, Winter 2020. https://doi.org/10.1216/jie.2020.32.457

Information

Received: 23 September 2019; Revised: 21 February 2020; Accepted: 2 March 2020; Published: Winter 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/jie.2020.32.457

Subjects:
Primary: 35R09, 35R11

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
21 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.32 • No. 4 • Winter 2020
Back to Top