Analytical and approximate approaches for generalized nonlinear Schrödinger equations involving the M-fractional derivative

BAYRAK M. A., DEMİR A.

Arabian Journal of Mathematics, vol.15, no.1, pp.115-128, 2026 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1007/s40065-025-00569-1
  • Journal Name: Arabian Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.115-128
  • Kocaeli University Affiliated: Yes

Abstract

The focus of this research is to achieve analytical and approximate solutions for generalized nonlinear fractional Schrödinger problems by residual power series method (RPSM). The fractional derivatives are taken as M-fractional derivative. This fractional derivative is a well-behaved derivative which is used in various fractional mathematical models. Various orders of Schrödinger equations are investigated in given examples. The obtained results and examples demonstrated the efficiency and accuracy of the proposed method. Moreover, illustrated graphs in examples verify the importance of the presented method.