Existence and uniqueness of holomorphic solutions for fractional Cauchy problem. (English) Zbl 1214.30027

Ibrahim, Rabha W.

J. Math. Anal. Appl. 380, No. 1, 232-240 (2011).

Summary: By employing majorant functions, the existence and uniqueness of holomorphic solutions to nonlinear fractional partial differential equations (Cauchy problems) are introduced. Furthermore, the analytic continuation of the solutions is studied.

MSC:

30E99	Miscellaneous topics of analysis in the complex plane
26A33	Fractional derivatives and integrals

Keywords:

fractional calculus; fractional differential operator; fractional integral operator; majorant function; fractional Cauchy problem in complex domain

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