On Effects of a New Method for Fractional Initial Value Problems

Kodal Sevindir H., Çetinkaya S., Demir A.

ADVANCES IN MATHEMATICAL PHYSICS, cilt.2021, ss.1-10, 2021 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2021
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1155/2021/7606442
  • Dergi Adı: ADVANCES IN MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1-10
  • Kocaeli Üniversitesi Adresli: Evet

Özet

The aim of this study is to analyze nonlinear Liouville-Caputo time-fractional problems by a new technique which is a combination of the iterative and ARA transform methods and is denoted by IAM. First, the ARA transform method and its inverse are utilized to get rid of time-fractional derivative. Later, the iterative method is applied to establish the solution of the problem in infinite series form. The main advantages of this method are that it converges to analytic solution of the problem rapidly and implementation of method is easy. Finally, outcomes of the illustrative examples prove the efficiency and accuracy of the method.