Abstract:Background. The purpose of the paper is the development of a computational algorithm for approximate recovery of derivative order in the generalized wave equation. Urgency of the stated problem is dictated not only by significant need for improvement of mathematical apparatus for solution of inverse and ill-posed problems but also by the growing number of applications of equations with partial derivatives of fractional order to mathematical modelling in different fields of physical and technical sciences. Materials and methods. The approach for solution of the stated problem is based on its reduction to a nonlinear in the unknown parameter integral equation and subsequent solution of this integral equation with the help of continuous operator method for solution of nonlinear equations in Banach spaces. Results. Application of the continuous operator equation made it possible to develop the numerical algorithm for recovery of fractional derivative order in the generalized wave equation on the extra assumption of that the solution of this equation is additionally known at one arbitrary point. Conclusions. The approach described in this paper appears to be quite efficient for solution of inverse problems for partial differential equations with fractional order derivatives. Extending of the used approach to a wider range of inverse and ill-posed problems for equations with fractional order derivatives is of considerable interest.
Keywords:generalized wave equation, fractional order Riemann-Liouville derivatives, inverse problems, continuous operator method, logarithmic norm, stability theory
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