A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate stability with respect to motion changes at fractional changes of variables. Note that dynamical systems, which are unstable ”in sense of Lyapunov”, can be stable w...

Here we study the univariate fuzzy fractional quantitative approximation of real valued functions on a compact interval by quasi-interpolation arctangent-algebraic-Gudermannian-generalized symmetrical activation function relied neural network operators. These approximations are derived establishing Jackson type inequalities involving moduli continuity right and left...

background : thymol and carvacrol have previously demonstrated larvicidal activity against aedes aegypti (diptera: culicidae). in view of this fact, it was of our interest to obtain synthetic derivatives and evaluate their larvicidal ac­tivity on ae. aegypti larvae. methods : structural modifications were performed on thymol and carvacrol in an effort to understand the functional groups necessa...

Systems of fractional-order differential equations present stability properties which differ in a substantial way from those systems integer order. In this paper, detailed analysis the linear fractional with Caputo derivative is proposed. Starting well-known Matignon’s results on single-order systems, for different proof provided together clarification limit case, investigation moved towards mu...

When defining a differential operator, one often employs, besides ordinary derivatives, generalized derivatives, which appear in a natural way when considering extensions of differential operators defined on differentiable functions, and weak derivatives, related to the transition to the adjoint operator [9]. Derivatives of fractional and negative orders appear when the differentiation is defin...

Based on molecular grand canonical ensemble density functional theory, we present a theoretical description of how reaction barriers and enthalpies change as atoms in the system are subjected to alchemical transformations, from one element into another. The change in the energy barrier for the umbrella inversion of ammonia is calculated along an alchemical path in which the molecule is transfor...