Nonlocal boundary value problems for hyperbolic equations with a Caputo fractional derivative

Elimhan N. Mahmudov; Shakir Sh Yusubov

doi:10.1016/j.cam.2021.113709

Nonlocal boundary value problems for hyperbolic equations with a Caputo fractional derivative

Elimhan N. Mahmudov^*, Shakir Sh Yusubov

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

In this paper, we study local and nonlocal boundary value problems for hyperbolic equations of general form with variable coefficients and a Caputo fractional derivative. To study the stated problem, a certain fractional-order functional space is introduced. The problem posed is reduced to an integral equation, and the existence of its solution is proved using an a priori estimate.

Original language	English
Article number	113709
Journal	Journal of Computational and Applied Mathematics
Volume	398
DOIs	https://doi.org/10.1016/j.cam.2021.113709
Publication status	Published - 15 Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Caputo derivative
Fractional derivative
Hyperbolic differential equation
Nonlocal problem
Riemann–Liouville integral

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10.1016/j.cam.2021.113709

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abstract = "In this paper, we study local and nonlocal boundary value problems for hyperbolic equations of general form with variable coefficients and a Caputo fractional derivative. To study the stated problem, a certain fractional-order functional space is introduced. The problem posed is reduced to an integral equation, and the existence of its solution is proved using an a priori estimate.",

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AU - Mahmudov, Elimhan N.

AU - Yusubov, Shakir Sh

PY - 2021/12/15

Y1 - 2021/12/15

N2 - In this paper, we study local and nonlocal boundary value problems for hyperbolic equations of general form with variable coefficients and a Caputo fractional derivative. To study the stated problem, a certain fractional-order functional space is introduced. The problem posed is reduced to an integral equation, and the existence of its solution is proved using an a priori estimate.

AB - In this paper, we study local and nonlocal boundary value problems for hyperbolic equations of general form with variable coefficients and a Caputo fractional derivative. To study the stated problem, a certain fractional-order functional space is introduced. The problem posed is reduced to an integral equation, and the existence of its solution is proved using an a priori estimate.

KW - Caputo derivative

KW - Fractional derivative

KW - Hyperbolic differential equation

KW - Nonlocal problem

KW - Riemann–Liouville integral

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DO - 10.1016/j.cam.2021.113709

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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ER -

Nonlocal boundary value problems for hyperbolic equations with a Caputo fractional derivative

Abstract

Bibliographical note

Keywords

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