New existence and uniqueness result for fractional Bagley-Torvik differential equation

  • Hamid Baghani, Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran,
  • Michal Feckan, Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynska dolina, 842 48 Bratislava, Slovakia;, and Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, 814 73 Bratislava, Slovakia.,
  • Javad Farokhi-Ostad, Department of Basic Sciences, Birjand University of Technology, Birjand, Iran.,
  • Jehad Alzabut, Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia., and Department of Industrial Engineering, OSTIM Technical University, Ankara 06374, Turkiye, and


Inspired by the paper of Fazli and Nieto in [Open Math. 17 (2019) 499–512], we establish new existence and uniqueness result for a type of fractional Bagley–Torvik differential equation. Reported result not only generalizes previous results but also adopts different technique. We finish this study by concluding remarks which discuss the preference of our theorem compared to previous results. An example is constructed with specific parameters that requires weaker conditions for the existence of a unique solution. Meanwhile, we construct an iterative sequence that converges to the unique solution and can not be commented via the results of Fazli and Nieto.

Vol. 23 (2022), No. 2, pp. 537-549
DOI: 10.18514/MMN.2022.3702

Download: MMN-3702