Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

*Correspondence: [email protected] 2Department of Mathematics, Yanbian University, Yanji, 133002, P.R. China Full list of author information is available at the end of the article Abstract In this paper, the concepts of a right fractional sum and right fractional difference operators are introduced. Some basic properties of a right fractional sum and right fractional difference operators are pr...

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...

Continuum extensions of common dual pairs of operators are presented and consolidated, based on the fractional Fourier transform. In particular, the fractional chirp multiplication, fractional chirp convolution, and fractional scaling operators are defined and expressed in terms of their common nonfractional special cases, revealing precisely how they are interpolations of their conventional co...

In this paper, boundary value problems of fractional order are converted into an optimal control problems. Then an approximate solution is constructed from translations and dilations of a B-spline function such that the exact boundary conditions are satisfied. The fractional differential operators are taken in the Riemann-Liouville and Caputo sense. Several example are given and the optimal err...

M. Saigo [Math. Rep. Coll. Gen. Educ., Kyushu Univ., 11 (1978) 135-143] has defined a pair of fractional integral operators and fractional derivatives involving generalizd hypergeometric function. The aim of present paper is to define their q-analogues. First, we define a pair of q-analogues of Saigo’s fractional integral operators and establish some results for it. Next, we define a pair of q-...

We prove duality between the left and right fractional derivatives, independently on the type of fractional operator. Main result asserts that the right derivative of a function is the dual of the left derivative of the dual function or, equivalently, the left derivative of a function is the dual of the right derivative of the dual function. Such duality between left and right fractional operat...

The aim of the present paper is to introduce and use the generalized exponential shift operators, operators on the base a (a > 0, = 1), to deal with the families of pseudo-Kampé de Fériet polynomials, which can be viewed as the natural complement for the theory of fractional derivatives and partial fractional differential equations of evolutive type. We show that these families allow the possib...

A class of fractional derivative operators (with the Appell hypergeometric function in the kernel) is used here to define a new subclass of analytic functions and a coefficient bound inequality is established for this class of functions. Also, an inclusion theorem for a class of fractional integral operators involving the Hardy space of analytic functions is proved. The concluding remarks brief...