Fractional calculus has many advantages. Under consideration of this paper is a (2+1)-dimensional non-linear local fractional heat conduction equation with arbitrary degree non-linearity. Backlund transformation reduced form the constructed by Painleve analysis. Based on transformation, some exact non-differentiable solutions are obtained. To gain more insights obtained solutions, two constrain...

We consider a family of exchange economies where consumers have multiprior preferences representing their ambiguity aversion. Under a linear independence assumption, we prove that regular economies are generic. Regular economies exhibit enjoyable properties: odd finite number of equilibrium prices, local constancy of this number and local differentiable selections of the equilibrium prices. Thu...

While conventional computational differentiation based on the forward or reverse modes allows highly accurate computation of derivatives, there are situations where these modes fail to produce the values of derivatives, although the underlying function is differentiable. Typical examples of this phenomenon are connected to the occurrence of branch points in coding as in IF-ELSE structures as we...

This paper considers global optimization with a black-box unknown objective function that can be non-convex and non-differentiable. Such a difficult optimization problem arises in many real-world applications, such as parameter tuning in machine learning, engineering design problem, and planning with a complex physics simulator. This paper proposes a new global optimization algorithm, called Lo...

Let m be a non zero element of N, f be a partial function from Rm to R, k be an element of N, and Z be a set. We say that f is continuously differentiable up to order of k and Z if and only if (Def. 1) (i) Z ⊆ dom f , and (ii) f is partial differentiable up to order k and Z, and (iii) for every non empty finite sequence I of elements of N such that len I ¬ k and rng I ⊆ Segm holds f Z is contin...