We present a map between squares and disks that associates concentric squares with concentric circles. This map preserves adjacency and fractional area, and has proven useful in many sampling applications where correspondences must be maintained between the two shapes. We also provide code to compute the map that minimizes branching and is robust for all inputs. Finally, we extend the map to th...

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...

This paper presents a dual of a general linear fractional functions programming problem. Dual is shown to be a linear programming problem. Along with other duality theorems, complementary slackness theorem is also proved. A simple numerical example illustrates the result.

In this article, a fuzzy goal programming (GP) and method of approximation is presented for the solution of a multiobjective linear plus linear fractional programming problem. In the proposed approach, membership functions are defined for each fuzzy goal and then a method of variable change on the underand overdeviational variables of the membership functions associated with the fuzzy goals of ...

In this paper we study linear fractional relations defined in the following way. Let Bi, B′ i, i = 1, 2, be Banach spaces. We denote the space of bounded linear operators by L. Let T ∈ L(B1 ⊕ B2,B 1 ⊕ B′ 2). To each such operator there corresponds a 2 × 2 operator matrix of the form T = ( T11 T12 T21 T22 ) , (∗) where Tij ∈ L(Bj,B i), i, j = 1, 2. For each such T we define a set-valued map GT f...

a procedure is presented that synthesizes fractional crystallization separation processes to obtain pure solids from multi-component solutions. the method includes a procedure to generate a network flow model to identify alternative process designs for fractional crystallization. the main advantage of this systematic procedure with respect to other reported procedures is using non-equilibrium s...

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter map is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spe...