The effect of the thermal radiation on MHD Casson fluid along with fractional derivative in an oscillating vertical plate is elucidated. More exactly, Caputo model utilized developing governing equations. Besides, influence buoyancy force due to temperature gradient has also been considered. derived partial differential equations are converted into ordinary by using Laplace transform technique ...

Unsteady magnetohydrodynamics (MHD) flow of fractionalized second grade nanofluid (Ag-Cu) over a vertical plate is obtained. The model solved by using CPC fractional derivative. novelty present study to generalized the Fourier’s and Fick’s laws. nanofluids are formed dispersing two different nanoparticles, silver (Ag) copper (Cu), into based fluid. governing dimensionless equations for velocity...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

The relationships between the generalized directional derivative of the distance function and the existence of nearest points as well as some geometry properties in Banach spaces are studied. It is proved in the present paper that the condition that for each closed subset G of X and x ∈ X \ G, the Clarke, Michel-Penot, Dini or modified Dini directional derivative of the distance function is 1 o...

It is proved that the class of operator equations F(y) = f solvable by a DSM (dynamical systems method) Newton-type method, u̇ = −[F (u) + a(t)I]−1[Fu(t) + a(t)u − f ], u(0) = u0, (∗) is large. Here F : X → X is a continuously Fréchet differentiable operator in a Banach space X , a(t) : [0, ∞) → C is a function, limt→∞ |a(t)| = 0, and there exists a y ∈ X such that F(y) = f . Under weak assumpti...

A new characterization of bivariate copulas is given by using the notion of Dini derivatives. Several examples illustrate the usefulness of this result.

In this paper, we show that higher-order optimality conditions can be obtain for arbitrary nonsmooth function. We introduce a new higher-order directional derivative and higher-order subdifferential of Hadamard type of a given proper extended real function. This derivative is consistent with the classical higher-order Fréchet directional derivative in the sense that both derivatives of the same...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gâteaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key elem...

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...