Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. These characteristics of the fractional derivatives make the fractional-order models more realistic and practical than the classical integer-order models. In recent years, boundary value problems for nonlinear fractional differential equations have been ad...

This paper investigates the existence and uniqueness of nontrivial solutions to a class of fractional nonlocal multi-point boundary value problems of higher order fractional differential equation, this kind of problems arise from viscoelasticity, electrochemistry control, porous media, electromagnetic and signal processing of wireless communication system. Some sufficient conditions for the exi...

*Correspondence: [email protected] Department of Mathematics, Hefei Normal University, Hefei, Anhui 230061, China Abstract In this paper, by means of the Avery-Peterson fixed point theorem, we establish the existence result of a multiple positive solution of the boundary value problem for a nonlinear differential equation with Riemann-Liouville fractional order derivative. An example illustrating...

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...