This paper presents a numerical solution of a class of fractional optimal control problems (FOCPs) in a bounded domain having a noise function by the spectral Ritz method‎. ‎The Bernstein polynomials with the fractional operational matrix are applied to approximate the unknown functions‎. ‎By substituting these estimated functions into the cost functional‎, ‎an unconstrained nonlinear optimizat...

In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we sho...

In this article, we investigate the analytical and approximate solutions for a fractional quadratic integral equation in frame of generalized Riemann–Liouville operator with respect to another function. The existence uniqueness results obtained. Moreover, some new special corresponding suitable values parameters ζ q are given. main proved by applying Banach’s fixed point theorem, Adomian decomp...

It is well-known that many business administration decision problems can be formulated as optimization problems. There are well over four hundred algo rithms to solve such problems. However, these algorithms are custom-made for each specific type of problem. This has lead to classification of problems, such as linear, fractional, quadratic, convex and non-convex programs. This paper pres ents a...

Recently Cambini and Carosi described a characterization of pseudolinearity of quadratic fractional functions. A reformulation of their result was given by Rapcsák. Using this reformulation, in this paper we describe an alternative proof of the Cambini–Carosi Theorem. Our proof is shorter than the proof given by Cambini–Carosi and less involved than the proof given by Rapcsák. As an application...