On the Inverse Problem of Time-Dependent Coefficient in a Time Fractional Diffusion Problem by Newly Defined Monic Laquerre Wavelets

Bayrak M. A., Demir A.

JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, cilt.18, sa.11, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 11
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1115/1.4063337
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, Civil Engineering Abstracts
  • Kocaeli Üniversitesi Adresli: Evet

Özet

The primary aim of this research is to establish the time-dependent diffusion coefficient in a one-dimensional time fractional diffusion equation in Caputo sense by means of newly defined Monic Laquerre wavelets (MLW) and collocation points. We first give the definition of MLW by taking Monic Laquerre's polynomials into account. Later, time fractional diffusion problem is reduced into a system of ordinary fractional and algebraic equations by utilizing MLW. The residual power series method (RPSM) and the overdetermined data are applied to this system to determine the solution and the unknown time-dependent coefficient together in series form. In the end, illustrative examples are presented to show the stability and accuracy of the proposed wavelet method for the inverse problem of determining unknown time-dependent coefficient in fractional diffusion problems. The reliability of the proposed algorithm for the inverse problems is supported by high degree of accuracy in the given examples.