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...

In the present study, vibration of cylindrical laminates with different layers and angles were studied. In order to actuate and polarize in radial direction, a piezoelectric layer was located at outer surface of composite shell. Laminates were assumed long enough so that plane strain state analysis in 2D can be used properly. In order to satisfy the boundary conditions, variables in terms of Fo...

We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The derivative was considered in the Caputo sense, while Riemann–Liouville integral operator used to give approximations unknown function and its derivatives. An operational matrix of integration introduced functions. By assuming that solution problem is s...

Abstract We investigate the properties of some recently developed variable-order differential operators involving order transition functions exponential type. Since characterization such is performed in Laplace domain, it necessary to resort accurate numerical methods derive corresponding behaviours time domain. In this regard, we develop a computational procedure solve fractional equations nov...