Bui NGHİA

8214

Existence of a mild solution to fractional differential equations with $\psi$-Caputo derivative, and its $\psi$-Hölder continuity

Existence of a mild solution to fractional differential equations with $\psi$-Caputo derivative, and its $\psi$-Hölder continuity

This paper is devoted to the study existence of locally/globally mild solutions for fractional differential equations with $\psi$-Caputo derivative with a nonlocal initial condition. We firstly establish the local existence by making use usual fixed point arguments, where computations and estimates are essentially based on continuous and bounded properties of the Mittag-Leffler functions. Secondly, we establish the called $\psi$-H\"older continuity of solutions, which shows how $|u(t')-u(t)|$ tends to zero with respect to a small difference $|\psi(t')-\psi(t)|^{\beta}$, $\beta\in(0,1)$. Finally, by using contradiction arguments, we discuss on the existence of a global solution or maximal mild solution with blowup at finite time.
Keywords:

Fractional calculus, Fractional differential equations, $\psi$-Caputo derivative, Fixed point theorem, Maximal mild solutions $\psi$-H\"older continuity.,

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Advances in the Theory of Nonlinear Analysis and its Application-Cover
  • Başlangıç: 2017
  • Yayıncı: Erdal KARAPINAR
Arşiv
Sayıdaki Diğer Makaleler

Existence of a mild solution to fractional differential equations with $\psi$-Caputo derivative, and its $\psi$-Hölder continuity

Bui NGHİA