نتایج جستجو برای: Generalized fractional derivatives

تعداد نتایج: 323879  

Journal: :Mathematical and Computer Modelling 2011
George A. Anastassiou

Here we prove fractional representation formulae involving generalized fractional derivatives, Caputo fractional derivatives and Riemann–Liouville fractional derivatives. Then we establish Poincaré, Sobolev, Hilbert–Pachpatte and Opial type fractional inequalities, involving the right versions of the abovementioned fractional derivatives.

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional deri...

This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for s...

2015
H. Roshanfekr

In this paper, the solution to Fuzzy sequential Fractional Initial Value Problem [FFIVP] under Caputo type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylors formu...

2013
Ahmad El-Ajou Omar Abu Arqub Zeyad Al Zhour Shaher Momani

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. New construction of the generalized Taylor’s power series is obtained. Some applicat...

Journal: :Entropy 2013
Ahmad El-Ajou Omar Abu Arqub Zeyad Abdel Aziz Al Zhour Shaher Momani

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. A new construction of the generalized Taylor’s power series is obtained. Some applic...

2001
G. A. ANASTASSIOU J. J. KOLIHA

This paper presents a class of Lp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor’s formula, which enables us to relax restrictions on the orders of fractional deriv...

2014
Hamid A. Jalab Rabha W. Ibrahim Jehad Alzabut

It is well known that the complex step method is a tool that calculates derivatives by imposing a complex step in a strict sense. We extended the method by employing the fractional calculus differential operator in this paper. The fractional calculus can be taken in the sense of the Caputo operator, Riemann-Liouville operator, and so forth. Furthermore, we derived several approximations for com...

نمودار تعداد نتایج جستجو در هر سال

با کلیک روی نمودار نتایج را به سال انتشار فیلتر کنید