scholarly journals Differential Sandwich Theorems with Generalised Derivative Operator

10.5772/8210 ◽  
2009 ◽  
Author(s):  
Maslina Darus ◽  
Khalifa Al-Shaqsi
Keyword(s):  
Derivative Operator

scholarly journals Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 850-856 ◽  
Author(s):  
Jun-Sheng Duan ◽  
Yun-Yun Xu
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Vibration System ◽  
Derivative Operator ◽  
Vibration Equation ◽  
State Response ◽  
Frequency Relation

Abstract The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator ${}_{-\infty} D_t^\beta,$where the order β is a real number satisfying 0 ≤ β ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < β < 1, while it contributes to the viscous inertia if 1 < β < 2. Thus the fractional derivative can represent the “spring-pot” element and also the “inerterpot” element proposed in the present article. The viscosity contribution coefficient, elasticity contribution coefficient, inertia contribution coefficient, amplitude-frequency relation, phase-frequency relation, and influence of the order are discussed in detail. The results show that fractional derivatives are applicable for characterizing the viscoelasticity and viscous inertia of materials.

scholarly journals Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samaira Naz ◽  
Muhammad Nawaz Naeem ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Derivative Operator ◽  
Practical Applications ◽  
Mathematical Problems ◽  
Grüss Type Inequalities

AbstractIn this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several mathematical problems relevant to practical applications.

scholarly journals A Fractional Approach to a Computational Eco-Epidemiological Model with Holling Type-II Functional Response

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1159
Author(s):  
B. Günay ◽  
Praveen Agarwal ◽  
Juan L. G. Guirao ◽  
Shaher Momani
Keyword(s):  
Numerical Method ◽  
Decision Makers ◽  
Derivative Operator ◽  
Research Fields ◽  
Fractional System ◽  
Chaotic Nature ◽  
And Control ◽  
The Impact ◽  
Distinguishing Features ◽  
Type Ii Functional Response

Eco-epidemiological can be considered as a significant combination of two research fields of computational biology and epidemiology. These problems mainly take ecological systems into account of the impact of epidemiological factors. In this paper, we examine the chaotic nature of a computational system related to the spread of disease into a specific environment involving a novel differential operator called the Atangana–Baleanu fractional derivative. To approximate the solutions of this fractional system, an efficient numerical method is adopted. The numerical method is an implicit approximate method that can provide very suitable numerical approximations for fractional problems due to symmetry. Symmetry is one of the distinguishing features of this technique compared to other methods in the literature. Through considering different choices of parameters in the model, several meaningful numerical simulations are presented. It is clear that hiring a new derivative operator greatly increases the flexibility of the model in describing the different scenarios in the model. The results of this paper can be very useful help for decision-makers to describe the situation related to the problem, in a more efficient way, and control the epidemic.

The derivative operator

1979 ◽  
Vol 9 (4-P1) ◽  
pp. 347-354 ◽  
Author(s):  
Kenneth E. Iverson
Keyword(s):  
Derivative Operator

Further extended Caputo fractional derivative operator and its applications

2017 ◽  
Vol 24 (4) ◽  
pp. 415-425 ◽  
Author(s):  
P. Agarwal ◽  
S. Jain ◽  
T. Mansour
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Derivative Operator

scholarly journals q-derivative operator proof for a conjecture of Melham

2014 ◽  
Vol 177 ◽  
pp. 158-164 ◽  
Author(s):  
Nadia N. Li ◽  
Wenchang Chu
Keyword(s):  
Derivative Operator

scholarly journals Approach of q-Derivative Operators to Terminating q-Series Formulae

2018 ◽  
Vol 26 (2) ◽  
pp. 99-111
Author(s):  
Xiaoyuan Wang ◽  
Wenchang Chu
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Operator Approach ◽  
Derivative Operator ◽  
Summation Formulae

AbstractThe q-derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric series.

scholarly journals An Extension of Caputo Fractional Derivative Operator by Use of Wiman’s Function

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2238
Author(s):  
Rahul Goyal ◽  
Praveen Agarwal ◽  
Alexandra Parmentier ◽  
Clemente Cesarano
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Derivative Operator ◽  
The Family ◽  
Generating Relations ◽  
Fractional Derivative Operators ◽  
Extended Operator ◽  
Two Parameter

The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag–Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relationships with extended hypergeometric functions in order to derive this extended operator. Due to symmetry in the family of special functions, it is easy to study their various properties with the extended fractional derivative operators.

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