Fractional viscoelastic models with Caputo generalized fractional derivative

2021 ◽  
Author(s):  
Nikita Bhangale ◽  
Krunal B. Kachhia ◽  
J. F. Gómez‐Aguilar
Keyword(s):  
Fractional Derivative ◽  
Viscoelastic Models ◽  
Generalized Fractional Derivative

scholarly journals The Principle of Differential Subordination and Its Application to Analytic and p-Valent Functions Defined by a Generalized Fractional Differintegral Operator

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1083 ◽  
Author(s):  
Nak Eun Cho ◽  
Mohamed Kamal Aouf ◽  
Rekha Srivastava
Keyword(s):  
Fractional Derivative ◽  
Integral Operators ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Family ◽  
Sandwich Type ◽  
Fractional Differintegral ◽  
Generalized Fractional Derivative ◽  
Fractional Differintegral Operator

A useful family of fractional derivative and integral operators plays a crucial role on the study of mathematics and applied science. In this paper, we introduce an operator defined on the family of analytic functions in the open unit disk by using the generalized fractional derivative and integral operator with convolution. For this operator, we study the subordination-preserving properties and their dual problems. Differential sandwich-type results for this operator are also investigated.

scholarly journals Homotopy Perturbation ρ-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation

2019 ◽  
Vol 3 (2) ◽  
pp. 14 ◽  
Author(s):  
Ndolane Sene ◽  
Aliou Niang Fall
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Generalized Fractional Derivative

In this paper, the approximate solutions of the fractional diffusion equations described by the fractional derivative operator were investigated. The homotopy perturbation Laplace transform method of getting the approximate solution was proposed. The Caputo generalized fractional derivative was used. The effects of the orders α and ρ in the diffusion processes was addressed. The graphical representations of the approximate solutions of the fractional diffusion equation and the fractional diffusion-reaction equation both described by the Caputo generalized fractional derivative were provided.

scholarly journals Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 94 ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Kamal Shah ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Condition ◽  
Hilfer Fractional Derivative ◽  
Fractional Differential ◽  
Generalized Fractional Derivative ◽  
Stability Results

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

scholarly journals ANALYSIS OF DENGUE FEVER OUTBREAK BY GENERALIZED FRACTIONAL DERIVATIVE

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040038
Author(s):  
PAUL BOSCH ◽  
J. F. GÓMEZ-AGUILAR ◽  
JOSÉ M. RODRÍGUEZ ◽  
JOSÉ M. SIGARRETA
Keyword(s):  
Fractional Derivative ◽  
Dengue Fever ◽  
Gaussian Model ◽  
Integral Operators ◽  
Real Data ◽  
Practical Application ◽  
Gaussian Models ◽  
Fractional Differential ◽  
Generalized Differential ◽  
Generalized Fractional Derivative

In this paper, we use the generalized fractional derivative in order to study the fractional differential equation associated with a fractional Gaussian model. Moreover, we propose new properties of generalized differential and integral operators. As a practical application, we estimate the order of the derivative of the fractional Gaussian models by solving an inverse problem involving real data on the dengue fever outbreak.

Universal fractional Euler-Lagrange equation from a generalized fractional derivate operator

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Rami El-Nabulsi
Keyword(s):  
Fractional Derivative ◽  
Variational Approach ◽  
Lagrange Equation ◽  
Derivative Operator ◽  
Hamilton Equations ◽  
Generalized Fractional Derivative

AbstractThe purpose of this paper is to extend the fractional actionlike variational approach by introducing a generalized fractional derivative operator. The generalized fractional formalism introduced through this work includes some interesting features concerning the fractional Euler-Lagrange and Hamilton equations. Additional attractive features are explored in some details.

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