In this paper a control problem for a controlled linear stochastic equation in a Hilbert space and an exponential quadratic cost functional of the state and the control is formulated and solved. The stochastic equation can model a variety of stochastic partial differential equations with the control restricted to the boundary or to discrete points in the domain. The solution method does not req...

This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.

Recently, fractional differential equations are applied widely in various fields of science and engineering. Regarding applications of fractional differential equations, we refer to 1– 15 and references cited therein. However, the investigation of basic theory of fractional differential equations is still not complete, and there is a great deal of work which needs to be done. Most of the invest...

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space ...

In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising inmathematical physics with local fractional derivative operators (LFDOs). To get approximate solutionsof these equations, we utilize the reduce differential transform method (RDTM) which is basedupon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. Theobtained ...

This paper is concerned with optimal control of linear backward stochastic differential equations (BSDEs) with a quadratic cost criteria, or backward linear-quadratic (BLQ) control. The solution of this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique. Two alternative, though equivalent, expressions for the optima...