Solvability of nonlinear pseudo‐parabolic equations involving generalized Caputo fractional derivatives

This study considers nonlinear fractional pseudo parabolic equations, which include the generalized Caputo fractional derivatives of a function with respect to an appropriate function, with general nonlocal initial conditions. Here, the fractional derivative is generalized from many well‐known ones,...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-10, Vol.47 (15), p.11846-11873
Main Authors: Minh Dien, Nguyen, Viet, Tran Quoc, Agarwal, Ravi P.
Format: Article
Language:English
Subjects:
Derivatives
differential equations
fixed point theorems
generalized Caputo fractional derivatives
Initial conditions
pseudo‐parabolic
Singularity (mathematics)
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This study considers nonlinear fractional pseudo parabolic equations, which include the generalized Caputo fractional derivatives of a function with respect to an appropriate function, with general nonlocal initial conditions. Here, the fractional derivative is generalized from many well‐known ones, such as the Caputo, Caputo–Katugampola, Caputo–Hadamard, Erdélyi–Kober, and Liouville–Caputo derivatives. We propose sufficient conditions to ensure that the problem has at least one or a unique mild solution. Furthermore, we investigate the continuous dependence of the mild solutions on the fractional order and other inputs. Particularly, source functions in this study may have temporal singularities. Finally, we provide numerical experiments to illustrate and confirm our theoretical findings.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9470