A sufficient condition for local controllability of a Caputo type fractional differential inclusion

A High Order Sufficient Condition for Local Controllability

a sufficient condition for null controllability of nonlinear control systems

classical control methods such as pontryagin maximum principle and bang-bang principle and other methods are not usually useful for solving opti-mal control systems (ocs) specially optimal control of nonlinear systems (ocns). in this paper, we introduce a new approach for solving ocns by using some combination of atomic measures. we define a criterion for controllability of lumped nonlinear con...

A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

A numerical method for solving a class of distributed order time-fractional diffusion partial differential equations according to Caputo-Prabhakar fractional derivative

In this paper, a time-fractional diffusion equation of distributed order including the Caputo-Prabhakar fractional derivative is studied. We use a numerical method based on the linear B-spline interpolation and finite difference method to study the solutions of these types of fractional equations. Finally, some numerical examples are presented for the performance and accuracy of the proposed nu...

A Sharp Sufficient Condition for Sparsity Pattern Recovery

Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...