Boundary Value Problems Of Fractional Order Research Articles

A new operational matrix for Legendre wavelets and its applications for solving fractional order boundary values problems

In this article, we generalize the Legendre wavelets operational matrix of derivatives to fractional order derivatives in the Caputo sense. Legendre wavelets and their properties are employed for deriving Legendre wavelets operational matrix of fractional derivatives and a general procedure for forming this matrix is introduced. Then truncated Legendre wavelets expansions together with these matrices are used for numerical solution of Bagley–Torvik fractional order boundary value problems. Several examples are included to demonstrate accuracy and applicability of the proposed method. Key words: Shifted Legendre polynomials, Legendre wavelets, Caputo derivative, fractional order boundary value problems.

An efficient method for solving non-linear singularly perturbed two points boundary-value problems of fractional order

In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade’ approximant of order [ m, m]. Some theoretical results are established and proved. Two numerical examples are discussed to illustrate the efficiency of the present scheme.

Solvability for fractional order boundary value problems at resonance

In this paper, by using the coincidence degree theory, we consider the following boundary value problem for fractional differential equation where denotes the Caputo fractional differential operator of order α, 2 < α ≤ 3. A new result on the existence of solutions for above fractional boundary value problem is obtained. Mathematics Subject Classification (2000): 34A08, 34B15.

Fractional order boundary value problem with integral boundary conditions involving Pettis integral

In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.

Solutions to a discrete, nonlinear, (N­1,1) fractional boundary value problem

We consider a discrete, nonlinear, ( N – 1, 1) fractional-order boundary value problem in one variable with a fractional-order derivative specified as the right boundary condition. We first derive and establish properties of the corresponding Green’s function and then apply these properties – together with Krasnosel’skii’s Theorem and Banach’s Contraction Mapping Theorem – to show the existence of a positive solution to the given problem.