The fractional variational calculus is a recent fifield, where classical problems are considered, but in the presence of derivatives. Since there several defifinitions derivatives, it logical to think different types optimality conditions. For this reason, order solve problems, two theorems necessary conditions well known: an Euler-Lagrange equation which involves Caputo and Riemann-Liouville o...

<p style='text-indent:20px;'>In this paper, one minimizes a fractional function over compact set. Using an exact separation theorem, gives necessary optimality conditions for strict optimal solutions in terms of Fréchet subdifferentials. All data are assumed locally Lipschitz.</p>

A fractional minimal cost flow problem under linear type belief degree based uncertainty is studied for the first time. This type of uncertainty is useful when no historical information of an uncertain event is available. The problem is crisped using an uncertain chance-constrained programming approach and its non-linear objective function is linearized by a variable changing approach. An illus...

In this paper, the solution to Fuzzy sequential Fractional Initial Value Problem [FFIVP] under Caputo type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylors formu...