Solutions to fractional differential equations that extend

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Fuzzy Local Fractional Differential Equations

Almost Automorphic Solutions to Abstract Fractional Differential Equations

Copyright q 2010 Hui-Sheng Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equat...

Oscillation of Solutions to Nonlinear Forced Fractional Differential Equations

In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...

Almost Automorphic Mild Solutions to Fractional Partial Difference-differential Equations

We study existence and uniqueness of almost automorphic solutions for nonlinear partial difference-differential equations modeled in abstract form as (∗) ∆u(n) = Au(n+ 1) + f(n, u(n)), n ∈ Z, for 0 < α ≤ 1 where A is the generator of a C0-semigroup defined on a Banach space X, ∆ denote fractional difference in Weyl-like sense and f satisfies Lipchitz conditions of global and local type. We intr...