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arXiv · 2308.03802

Fractional Telegraph equation with the Riemann-Liouville derivative

Rajapboy Saparbayev
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Abstract

The Telegraph equation $(\partial_{t}^{\rho })^{2}u(x,t)+2\alpha \partial_{t}^{\rho }u(x,t)-u_{xx}(x,t)=f(x,t)$, where $0<t\leq T$ and $0<\rho<1$, with the Riemann-Liouville derivative is considered. Existence and uniqueness theorem for the solution to the problem under consideration is proved. Inequalities of stability are obtained. The applied method allows us to study a similar problem by taking instead of $d^2/dx^2$ an arbitrary elliptic differential operator $A(x, D)$, having a compact inverse.

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Rajapboy Saparbayev. 2023-08-06. Fractional Telegraph equation with the Riemann-Liouville derivative. https://arxiv.org/abs/2308.03802

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