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Open Access Research

A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions

Khaled M Furati

Author affiliations

Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

Citation and License

Boundary Value Problems 2012, 2012:58  doi:10.1186/1687-2770-2012-58

Published: 17 May 2012

Abstract

A Cauchy-type nonlinear problem for a class of fractional differential equations with sequential derivatives is considered in the space of weighted continuous functions. Some properties and composition identities are derived. The equivalence with the associated integral equation is established. An existence and uniqueness result of the global continuous solution is proved.

AMS Subject Classification: 26A33; 34A08; 34A34; 34A12; 45J08.

Keywords:
fractional derivatives; Riemann-Liouville fractional derivative; sequential fractional derivative; fractional differential equation