On multi-order fractional differential operators in the unit disk

Approximate Solutions for Fractional Differential Equation in the Unit Disk

Recently, fractional differential equations and inclusions have been of great interest. It is caused both by the intensive development of the theory of fractional calculus [9] itself and by the applications of such constructions in various sciences and topics such as physics, mechanics, chemistry, engineering, control systems, etc. [1,4,10,11,12,18]. Moreover, fractional differential equations ...

Study on multi-order fractional differential equations via operational matrix of hybrid basis functions

In this paper we apply hybrid functions of general block-pulse‎ ‎functions and Legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (FDEs)‎. ‎Our approach is based on incorporating operational matrices of‎ ‎FDEs with hybrid functions that reduces the FDEs problems to‎ ‎the solution of algebraic systems‎. ‎Error estimate that verifies a‎ ‎converge...

Variational formulation of problems involving fractional order differential operators

In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). These fractional derivatives lead to non-symmetric boundary value problems, which are investigated from a variational point of view. The variational problem for the Riemann-Liouville case is coercive on the space H α/2 0 (0, 1) but the ...

High-order Green operators on the disk and the polydisc

On the Numerical Solution of One Dimensional Schrodinger Equation with Boundary Conditions Involving Fractional Differential Operators

In this paper we study of collocation method with Radial Basis Function to solve one dimensional time dependent Schrodinger equation in an unbounded domain. To this end, we introduce artificial boundaries and reduce the original problem to an initial boundary value problem in a bounded domain with transparent boundary conditions that involves half order fractional derivative in t. Then in three...