arXiv subjects

M. Şan

Publications and source records attributed to M. Şan.

2 recordsLinked to original sources

arXiv2020

Existence and Uniqueness Results for a nonlinear fractional differential equations of order $σ\in(1,2)$

The main objective of this article is to discuss the local existence of the solution to an initial value problem involving a non-linear differential equation in the sense of Riemann-Liouville fractional derivative of order $σ\in(1,2),$ when the nonlinear term has a discontinuity at zero. Hereafter, by using some tools of Lebesgue spaces such as Hölder inequality, we obtain Nagumo-type, Krasnoselskii-Krein-type and Osgood-type uniqueness theorems for the problem.

math.AP↗

arXiv2017

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

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 $0<R\leq 1.$

math.CV↗