☆ 4.7 Article

Fractional Telegraph Equation with the Caputo Derivative

FRACTAL AND FRACTIONAL (2023)

An efficient numerical scheme for fractional model of telegraph equation

M. S. Hashmi et al.

Summary: This study proposes a novel approach for the numerical solution of the fractional telegraph equation using a combination of differential quadrature method and modified cubic B-spline. The stability of the proposed scheme is ensured using a matrix-based technique, and the feasibility and applicability of the algorithm are demonstrated through test problems.

ALEXANDRIA ENGINEERING JOURNAL (2022)

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Article Mathematics

Initial-boundary Value Problem for a Time-fractional Subdiffusion Equation with an Arbitrary Elliptic Differential Operator

R. R. Ashurov et al.

Summary: This study considers an initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator. The uniqueness and existence of the classical solution are proved using the classical Fourier method, and sufficient conditions for convergence of the corresponding Fourier series are indicated. In the case of an initial-boundary value problem on an N-dimensional torus, it is shown that these conditions are not only sufficient but also necessary.

LOBACHEVSKII JOURNAL OF MATHEMATICS (2021)

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Article Mathematics