On the solvability fractional of a boundary value problem with new fractional integral

Bekkouche M. M., Guebbai H., KURULAY M.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, vol.64, pp.551-564, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64
  • Publication Date: 2020
  • Doi Number: 10.1007/s12190-020-01368-x
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.551-564
  • Keywords: Fractional Boundary value problem, Green's function, Fractional derivative, fractional integral
  • Yıldız Technical University Affiliated: Yes


This work presents new techniques for finding solutions of linear fractional differential equation boundary value problem when the derivation is conformable fractional of Caputo type, the first technique we will study the method that converts an initial value problem to an equivalent linear ordinary differential equation of second order. In order to find solution by an other technique we introduce a new definition of fractional integral as an inverse of the conformable fractional derivative of Caputo. Also, some examples are included to improve the validity and applicability of the techniques.