Abstract: This paper presents an accurate numerical method for solving a class of fractional optimal control problems (FOCPs). The fractional derivative in these problems is in the Caputo sense. In this technique, we approximate FOCPs and end up with a finite dimensional problem. The method is based on the combination of the useful properties of Chebyshev polynomials approximation and finite di...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...

In this paper, we establishes certain new weighted Young and P?lya-Szeg?-type inequalities involving Marichev-Saigo-Maeda fractional integral operators. Meanwhile, corresponding Cauchy-Schwarz type inequalities, Shisha-Mond Diaz-Metcalf for operators are also obtained. As applications, some estimates Chebyshev-type with two unknown functions presented. The main results of paper more general inc...

In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...

This paper presents some new propositions related to the fractional order h-difference operators, for case of general quadratic forms and polynomial type, which allow proving stability systems, by means discrete Lyapunov direct method, using functions, functions any positive integer order, respectively. Some examples are given illustrate these results.

In this paper, we introduce the generalized left-side and right-side fractional integral operators with a certain modified ML kernel. We investigate Chebyshev inequality via general family of operators. Moreover, derive new results type inequalities for finite products functions. addition, establish an estimate functional by using From our above-mentioned results, find similar some specialized ...

We provide an algorithm to compute the nodes and weights for Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary real poles outside [−1, 1]. Contrary to existing rational quadrature formulas, the computational effort is very low, even for extremely high degrees, and under certain conditions on the poles it can be shown that the complexity is of...