Existence and extremal solutions in Banach algebras for a fractional order differential equation
Abstract
The existence of a solution in Banach algebras for a fractional order nonlinear quadratic differential equation with initial value condition is investigated in this paper. Furthermore, we demonstrate that the solutions to this equation are appealing locally. The primary conclusion is established using basic hybrid fixed point theory methods for three operators. Under certain monotonicity criteria, existence theorems for extremal solutions can also be established. Finally, we provide a specific example to demonstrate our findings.
Copyright © 2022 S. P. Shinde, B. D. Karande. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. P. Shinde, B. D. Karande, Existence and extremal solutions in Banach algebras for a fractional order differential equation, J. Math. Comput. Sci. 12 (2022), 157. https://doi.org/10.28919/jmcs/7304
BibTeX
@article{Shinde2022,
author = {Shinde, S. P. and Karande, B. D.},
title = {Existence and extremal solutions in Banach algebras for a fractional order differential equation},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {157},
doi = {10.28919/jmcs/7304}
}