Pipeline are known as the most reliable and economical mode of transportation for petroleum and its derivatives, especially when large amounts of products have to be pumped for large distances. In this work we address the short-term schedule of a pipeline system comprising the distribution of several petroleum derivatives from a single oil refinery to several depots, connected to local consumer...

At present, fractional differential is the effective mathematical approach which deals with factual problems. This projected technique employs derivatives definitions Riemann-Liouville (R-L), Grunwald-Letnikov (G-L) and caputo for denoising medical image. The presented method based on derivative in turn improves quality of input image processed integer order such as pre-processing operation, co...

This paper provides both analytical and numerical solutions of (PDEs) involving time-fractional derivatives. We implemented three powerful techniques, including the modified variational iteration technique, Adomian decomposition homotopy analysis to obtain an approximate solution for bounded space variable ν. The Laplace transformation is used in derivative operator enhance proposed methods’ pe...

Generalized constitutive relationships of viscoelastic foams are investigated in which the time derivatives of integer order are replaced by derivatives of fractional order. To this point, the justification of such models has resided in the fact that they are effective in describing the behavior of real materials. In this work, the three-parameter fractional Kelvin Voigt model is compared to th...

Tthis paper, is concerned with obtaining numerical solutions for a class of convection-diffusion equations (CDEs) with variable coefficients. Our approaches are based on collocation methods. These approaches implementing all four kinds of shifted Chebyshev polynomials in combination with Sinc functions to introduce an approximate solution for CDEs . This approximate solution can be expressed as...

In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples...

We associate with a Bienaymé-Galton-Watson branching process a family tree rooted at the ancestor. For a positive integer N , define a complete N -ary tree to be the family tree of a deterministic branching process with offspring generating function s . We study the random variables VN,n and VN counting the number of disjoint complete N -ary subtrees, rooted at the ancestor, and having height n...

In some real world problems, fractional-order models are found to be more adequate than integer-order models. Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. The mathematical modelling of systems and processes in the fields of physics, chemistry, aerodynamics, electro dynamics of complex medium, polymer...

We provide a general notion of a Digital Derivative in 1−dimensional grids, which has real or integer-only versions. From any such masks, a family of masks called skipping masks are defined. We prove general results of multigrid convergence for skipping masks. We propose a few examples of digital derivative masks, including the now well-known binomial mask. The corresponding skipping masks auto...