Furati, Khaled M. A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions. (English) Zbl 1279.26016 Bound. Value Probl. 2012, Paper No. 58, 14 p. (2012). Summary: 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. Cited in 4 Documents MSC: 26A33 Fractional derivatives and integrals 34A08 Fractional ordinary differential equations and fractional differential inclusions 34A34 Nonlinear ordinary differential equations and systems, general theory 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations Keywords:fractional derivatives; Riemann-Liouville fractional derivative; sequential fractional derivative; fractional differential equation PDF BibTeX XML Cite \textit{K. M. Furati}, Bound. Value Probl. 2012, Paper No. 58, 14 p. (2012; Zbl 1279.26016) Full Text: DOI References: [1] doi:10.1016/j.camwa.2009.05.010 · Zbl 1189.34152 · doi:10.1016/j.camwa.2009.05.010 [2] doi:10.1007/s10958-010-0087-7 · Zbl 1305.34007 · doi:10.1007/s10958-010-0087-7 [3] doi:10.1016/j.na.2010.06.088 · Zbl 1205.26013 · doi:10.1016/j.na.2010.06.088 [4] doi:10.1016/j.camwa.2011.07.025 · Zbl 1231.34007 · doi:10.1016/j.camwa.2011.07.025 [5] doi:10.1016/j.camwa.2011.03.008 · Zbl 1228.34022 · doi:10.1016/j.camwa.2011.03.008 [6] doi:10.1016/S0301-0104(02)00670-5 · doi:10.1016/S0301-0104(02)00670-5 [7] doi:10.1016/S0020-7462(01)00121-4 · Zbl 1346.76009 · doi:10.1016/S0020-7462(01)00121-4 [8] doi:10.1088/1751-8113/43/5/055204 · Zbl 1379.74012 · doi:10.1088/1751-8113/43/5/055204 [9] doi:10.1088/0022-3727/39/18/022 · doi:10.1088/0022-3727/39/18/022 [10] doi:10.1103/PhysRevE.51.R848 · doi:10.1103/PhysRevE.51.R848 [11] doi:10.1090/S0002-9947-09-04678-9 · Zbl 1186.60079 · doi:10.1090/S0002-9947-09-04678-9 [12] doi:10.1016/S0378-4371(00)00255-7 · doi:10.1016/S0378-4371(00)00255-7 [13] doi:10.1007/s11006-005-0003-5 · Zbl 1086.34050 · doi:10.1007/s11006-005-0003-5 [14] doi:10.1134/S000143460711003X · Zbl 1160.34053 · doi:10.1134/S000143460711003X [15] doi:10.3103/S1066369X09090011 · Zbl 1188.47038 · doi:10.3103/S1066369X09090011 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.