We revisit some basic concepts and ideas of the classical differential calculus convex analysis extending them to a broader frame. reformulate generalize notion Gateaux differentiability propose new notions generalized derivative subdifferential in an arbitrary topological vector space. Meaningful examples preserving key properties original are provided.

We establish the generalized Evans–Krylov and Schauder type estimates for nonlocal fully nonlinear elliptic equations with rough kernels of variable orders. In contrast to fractional Laplacian operators having a fixed order differentiability ??(0,2), under consideration have orders differentiability. Since is not characterized by single number, we consider function ? describing differentiabilit...

In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method. Keywords—Fuzzy differential equation, Generalized ...

In this paper, we consider Simultaneous Perturbation Stochastic Approximation (SPSA) for function minimization. The standard assumption for convergence is that the function be three times differentiable, although weaker assumptions have been used for special cases. However, all work that we are aware of at least requires differentiability. In this paper, we relax the differentiability requireme...