Implicit fractional differential equations: Existence of a solution revisited

Çelik C., DEVELİ F.

Mathematical Methods in the Applied Sciences, vol.47, no.6, pp.5090-5097, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 6
  • Publication Date: 2024
  • Doi Number: 10.1002/mma.9856
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.5090-5097
  • Keywords: differentials equations, existence of solution, fixed point theorem, fractional derivative
  • Yıldız Technical University Affiliated: Yes

Abstract

This paper focuses on revisiting and improving the results regarding the existence of a solution to the implicit fractional differential equations (FDEs) given in the following form: (Formula presented.) for all (Formula presented.) with the initial condition (Formula presented.), where (Formula presented.) is the Caputo fractional derivative (CFD). Mainly, we aim to weaken the necessary conditions often found in the literature for guaranteeing the existence of solution.