In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann– Liouville fractional deri...

The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal contro...

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 cond...

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transport...

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends only on the left Riemann–Liouville fractional ...

Our motivation is the question how similar the f -colouring problem is to the classic edge-colouring problem, particularly with regard to graph parameters. In 2010, Zhang, Yu, and Liu [9] gave a new description of the f -matching polytope and derived a formula for the fractional f -chromatic index, stating that the fractional f -chromatic index equals the maximum of the fractional maximum f -de...

A new method is proposed to find an optimal intuitionistic fuzzy solution to fully intuitionistic fuzzy linear fractional programming (IFLFP) problem, in which ranking functions are not used. Here, the IFLFP problem is transformed into an equivalent crisp linear fractional programming problem which is then solved by linear programming (LP) technique and / or linear fractional programming techni...

Parameter estimation for fractional-order chaotic systems has been an interesting and important issue in theory and various fields of application. In this paper, fractional orders, as well as systematic parameters of fractional-order chaotic systems are considered by treating fractional orders as additional parameters. The parameter estimation is transformed into a multidimensional optimization...

Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately described by fractional differential equations, which involves fractional derivatives in time or/and space. The fractional derivatives describe either history mechan...