This paper presents a general formulation and numerical scheme for Fractional Optimal Control Problem (FOCP) of a distributed system in cylindrical coordinate and uses a hollow cylinder with axial symmetry as the example to demonstrate the method. The fractional derivatives are expressed in the Caputo-Sense. The performance index of FOCP is considered as a function of both the state and the con...

In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that conditions provided by one-sided Laplace transform not those required for Riemann-Liouville Caputo derivatives. The solved with generality as well applied continuous-time fractional autoregressive-moving average systems.

Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann...

In this article, we use the homotopy perturbation method and Adomian decomposition with Yang transformation to discover analytical solution time-fractional coupled Schrödinger–KdV equation. Caputo sense, fractional derivatives are described. A convergent series is used calculate solutions of PDEs. Analytical results achieved applying techniques numerically calculated represented in form tables ...

The brain, a mixture of neural and glia cells, vasculature, and cerebrospinal fluid (CSF), is one of the most complex organs in the human body. To understand brain responses to traumatic injuries and diseases of the central nervous system it is necessary to develop accurate mathematical models and corresponding computer simulations which can predict brain biomechanics and help design better dia...

Email: [email protected] Abstract: In this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equat...

In this paper, an approximate formula of the fractional derivatives (Caputo sense) is derived. The proposed formula is based on the generalized Laguerre polynomials. Special attention is given to study the convergence analysis of the presented formula. The spectral Laguerre collocation method is presented for solving a class of fractional optimal control problems (FOCPs). The properties of Lagu...

and Applied Analysis 3 The left Caputo fractional derivative is C aD f t 1 Γ n − α ∫ t a t − τ n−α−1 ( d dτ )n f τ dτ, 2.6 while the right Caputo fractional derivative is

A fractional wave equation replaces the second time derivative by a Caputo derivative of order between one and two. In this paper, we show that the fractional wave equation governs a stochastic model for wave propagation, with deterministic time replaced by the inverse of a stable subordinator whose index is one half the order of the fractional time derivative.