Global Conference on Mathematics and Applications (GCMA)

\textbf{Abstract.}
We establish well-posedness and strong stability for a degenerate wave equation with tempered fractional damping, complemented by an fPINN numerical approximation.

\textbf{Keywords:} Degenerate wave equation; tempered Caputo damping; $C_0$-semigroup; strong stability; fPINN.

\section{Model and Main Results}

Let $\Omega=(0,1)$ and consider
[
u_{tt}-(x^m...

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Abstract
The main objective of this work is to prove the existence, unique
ness of the mild solution for abstract hybrid fractional diffusion equa
tions by using the resolvent operators and fixed point theorems. More
over, we studied an example on partial differential equation with Ca
puto fractional derivative.
Keywords: Caputo fractional derivative, Abstract hybrid equation,...

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This paper is concerned with a nonlinear wave equation with logarithmic damping

and logarithmic source terms. Using the Faedo–Galerkin method, compactness tech-
niques, and monotonicity arguments, we establish the local existence and uniqueness

of the solution. We further derive energy estimates to analyze the interplay between
dissipation and nonlinear source effects, proving the...

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*Abstract
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Keywords*
Elliptic equations, Critical Sobolev exponent , Compact Rienmannin manifolds, Plais-Smale condition,...

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\begin{equation}
\left{
\begin{array}{ll}
\mathbf{Y}{tt}-\gamma \Delta \mathbf{Y}-(\alpha +\gamma )\nabla (\operatorname{div} \mathbf{Y})+\alpha
{1}\mathbf{Y}{t}+\alpha {2}\mathbf{Y}{t}(t-\tau {1})=F_{1}(Y,Z), &
x\in...

The incorporation of memory effects into epidemic models has become
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sion...

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from the concepts of intuitionistic fuzzy set. For more than a...

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\begin{equation*}
...

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\begin{equation}
\sigma_{e}(n) = \sum_{i=1, \, 2 \mid i}^{\tau(n)} d_i \text{ and }\sigma_{o}(n) = \sum_{i=1, \, 2 \nmid i}^{\tau(n)} d_i.
\end{equation}
Note that the sequences...

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