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

Mahmudov E. , Yusubov S. S.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.398, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 398
  • Publication Date: 2021
  • Doi Number: 10.1016/j.cam.2021.113709
  • Title of Journal : JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Keywords: Hyperbolic differential equation, Fractional derivative, Riemann-Liouville integral, Caputo derivative, Nonlocal problem, PARTIAL-DIFFERENTIAL-EQUATIONS, DARBOUX PROBLEM, HIGH-ORDER, APPROXIMATION, INCLUSIONS

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. (C) 2021 Elsevier B.V. All rights reserved.