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An operator theoretical approach to Riemann‐Liouville fractional Cauchy problem
Author(s) -
Mei ZhanDong,
Peng JiGen,
Zhang Yang
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200191
Subject(s) - mathematics , operator (biology) , cauchy–riemann equations , resolvent , cauchy problem , fractional calculus , initial value problem , mathematical analysis , cauchy distribution , pure mathematics , biochemistry , chemistry , repressor , transcription factor , gene
This paper is concerned with developing an operator theory for Riemann‐Liouville fractional Cauchy problem. Two notions, named Riemann‐Liouville fractional resolvent and solution operator, are developed. Some of their properties are deduced. Moreover, the obtained results are applied to Riemann‐Liouville fractional Cauchy problem.