BASIC THEORY FOR DIFFERENTIAL EQUATIONS WITH UNIFIED REIMANN-LIOUVILLE AND HADAMARD TYPE FRACTIONAL DERIVATES

KARPUZ B., ÖZKAN U. M., Yalcin T., Yildiz M. K.

INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, vol.13, no.2, pp.216-230, 2017 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2017
  • Journal Name: INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.216-230
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this paper, we extend the definition of the fractional integral and derivative introduced in [Appl. Math. Comput. 218 (2011)] by Katugampola, which exhibits nice properties only for numbers whose real parts lie in [0,1]. We prove some interesting properties of the fractional integrals and derivatives. Based on these properties, the following concepts for the new type fractional differential equations are explored: Existence and uniqueness of solutions; Solutions of autonomous fractional differential equations; Dependence on the initial conditions; Greens function; Variation of parameters formula.