A. The von Mises Expansion Before diving into the auxiliary results of Section 5, let us first derive some properties of the von Mises expansion. It is a simple calculation to verify that the Gateaux derivative is simply the functional derivative of in the event that T (F ) = R (f). Lemma 8. Let T (F ) = R (f)dμ where f = dF/dμ is the Radon-Nikodym derivative, is differentiable and let G be som...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

The controlling kinetics of the water solubility of two synthesized mono azo naphthalimide based disperse dyestuffs in the presence of two different dispersing agents namely Irgasol DAM and lyoprint EV agents at various temperatures were investigated. An exponential rate equation was found to describe the dissolution process. The addition of Irgasol DAM and Lyoprint EV dispersing agents increas...

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.

The purpose of this paper is to study the fuzzy fractional differentialequations. We prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. Fuzzy derivative is considerin the Goetschel-Voxman sense and fractional derivative is consider in theRiemann Liouville sense. At the end, we...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...