Various discussions have been made by many investigators on the motor effect produced by stimulation of the splanchnic nerve which has been almost universally noted to be the inhibitory nerve to the stomach and small intestine (Kuntz1953, Hukuhara1953). Many workers have speculated as to whether or not the intensity, frequency and type of stimulation (Brown, McSwiney and Wadge1930, Barry1932, H...

Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, ar...

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to khypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol’skii class and the generalized Lipschitz class. To define the Weyl-Nikol’skii class, we use the concept of a (λ, β)-derivative, which is a generalization of the derivative in the sense ...

Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

M. H. Al-Abbadi and M. Darus 2009 recently introduced a new generalized derivative operator μ λ1 ,λ2 , which generalizedmany well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit disk U {z ∈ C : |z| < 1} which is defined by new generalized derivative operator. Some results on coefficient ...

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent fun...

In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the socalled generalized Weyl-Nikol’skii class and the generalized Lipschitz class. To define the Weyl-Nikol’skii class, we use the concept of a (λ, β)-derivative, which is a generalization of the derivative in the sense o...

This report is concerned with a control problem associated to a semilinear second order ordinary diierential equation with pointwise state constraints. The control acts as a coeecient of the state equation. The nonlinear part of the equation is governed by a Nemytskij operator deened by a nonsmooth function. We prove the existence of optimal controls and obtain a necessary optimality condition ...