Boundary control for a class of pseudo-parabolic differential equations

The variational iteration method for a class of tenth-order boundary value differential equations

Existence of positive solution to a class of boundary value problems of fractional differential equations

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

Parameter determination in a parabolic inverse problem in general dimensions

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

A New Modification of Legendre-Gauss Collocation Method for Solving a Class of Fractional Optimal Control Problems

In this paper, the optimal conditions for fractional optimal control problems (FOCPs) were derived in which the fractional differential operators defined in terms of Caputo sense and reduces this problem to a system of fractional differential equations (FDEs) that is called twopoint boundary value (TPBV) problem. An approximate solution of this problem is constructed by using the Legendre-Gauss...

Optimal Control of a Class of Parabolic Partial Differential Equations

In this paper we, apply the classical control theory to a parabolic partial differential equation in a bounded domain with diffusivity-interior-boundary actuation. We first we study the existence of the solution of the parabolic partial differential equation, then we study the solution bound estimate which are used to prove the existence of the solution of the optimal control problem in a Banac...