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...
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| Vydáno v: | European journal of pure and applied mathematics Ročník 18; číslo 3; s. 6238 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
01.08.2025
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| ISSN: | 1307-5543, 1307-5543 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
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| ISSN: | 1307-5543 1307-5543 |
| DOI: | 10.29020/nybg.ejpam.v18i3.6238 |