The New Existence and Uniqueness Results for Complex Nonlinear Fractional Differential Equation

2015/12/15 by M. Şan, Şan, M., K. N. Soltanov +1
Mathematics · #30A10 #30C45 #30C55 #35G10 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:30A10 #msc:30C45 #msc:30C55 #msc:35G10

paper · pdf · doi:10.48550/arxiv.1512.04780

16 pages

arxiv created 2017/07/15 · arxiv updated 2017/07/18

Abstract

In this article, we obtain existence and uniqueness results to some problems involving complex nonlinear fractional differential equations (FDEs) in the closed unit disc of C. By help of these results, we prove that some IVPs for some fractional differential equations with Caputo or Riemann-Liouville derivative admit at least one local (or unique) solution continuous on a closed interval [0,R] and real analytic on (0,R), where 0<R≤ 1.

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