Finite Rank Solution for Conformable Second-Order Abstract Cauchy Problem in Hilbert Space
This paper presents a comprehensive analytical framework for constructing finite-rank solution to second-order conformable fractional abstract Cauchy problem. We examine the mathematical structure:% \begin{equation*} Eu^{(2\alpha )}(t)+Au^{(\alpha )}(t)+Bu(t)=f(t) \end{equation*} subject to prescrib...
Saved in:
| Published in: | European journal of pure and applied mathematics Vol. 18; no. 3; p. 6238 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.08.2025
|
| ISSN: | 1307-5543, 1307-5543 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | This paper presents a comprehensive analytical framework for constructing finite-rank solution to second-order conformable fractional abstract Cauchy problem. We examine the mathematical structure:% \begin{equation*} Eu^{(2\alpha )}(t)+Au^{(\alpha )}(t)+Bu(t)=f(t) \end{equation*} subject to prescribed initial conditions $u(0)=u_{0}$ and $u^{(\alpha )}(0)=u_{0}^{(\alpha )},$ where $A,$ $B$ and $E$ represent closed linear operators acting on a Banach space $X,$ $f:[0,\infty )\rightarrow X$ is continuous, and $u$ is continuously differentiable on $[0,\infty ).$ Our analytical methodology exploits tensor product decomposition techniques to transform the problem into finite-dimensional systems. This work proves solution existence and uniqueness under specific conditions, and provides computational methods for many types of this problem. |
|---|---|
| ISSN: | 1307-5543 1307-5543 |
| DOI: | 10.29020/nybg.ejpam.v18i3.6238 |