scholarly journals Some comments on using fractional derivative operators in modeling non-local diffusion processes

2021 ◽  
Vol 381 ◽  
pp. 113040 ◽  
Author(s):  
T. Namba ◽  
P. Rybka ◽  
V.R. Voller
Keyword(s):  
Fractional Derivative ◽  
Diffusion Processes ◽  
Non Local ◽  
Fractional Derivative Operators ◽  
Local Diffusion

scholarly journals On the parabolic Harnack inequality for non-local diffusion equations

2019 ◽  
Vol 295 (3-4) ◽  
pp. 1751-1769 ◽  
Author(s):  
Dominik Dier ◽  
Jukka Kemppainen ◽  
Juhana Siljander ◽  
Rico Zacher
Keyword(s):  
Harnack Inequality ◽  
Diffusion Equations ◽  
Parabolic Harnack Inequality ◽  
Non Local ◽  
Local Diffusion

scholarly journals A meshless Galerkin method for non-local diffusion using localized kernel bases

2018 ◽  
Vol 87 (313) ◽  
pp. 2233-2258 ◽  
Author(s):  
R. B. Lehoucq ◽  
F. J. Narcowich ◽  
S. T. Rowe ◽  
J. D. Ward
Keyword(s):  
Galerkin Method ◽  
Non Local ◽  
Local Diffusion ◽  
Meshless Galerkin Method

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.

scholarly journals Hardy-Type Inequalities for an Extension of the Riemann- Liouville Fractional Derivative Operators

2021 ◽  
Vol 45 (5) ◽  
pp. 797-813
Author(s):  
SAJID IQBAL ◽  
◽  
GHULAM FARID ◽  
JOSIP PEČARIĆ ◽  
ARTION KASHURI
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Mean Value ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Liouville Fractional Derivative ◽  
Fractional Derivative Operators

In this paper we present variety of Hardy-type inequalities and their refinements for an extension of Riemann-Liouville fractional derivative operators. Moreover, we use an extension of extended Riemann-Liouville fractional derivative and modified extension of Riemann-Liouville fractional derivative using convex and monotone convex functions. Furthermore, mean value theorems and n-exponential convexity of the related functionals is discussed.

scholarly journals Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Mostafa Tahiri ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Optimality Conditions ◽  
Fractional Derivatives ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Derivative Operator ◽  
Sir Epidemic ◽  
Non Local

<p style='text-indent:20px;'>The main aim of the present work is to study and analyze a reaction-diffusion fractional version of the SIR epidemic mathematical model by means of the non-local and non-singular ABC fractional derivative operator with complete memory effects. Existence and uniqueness of solution for the proposed fractional model is proved. Existence of an optimal control is also established. Then, necessary optimality conditions are derived. As a consequence, a characterization of the optimal control is given. Lastly, numerical results are given with the aim to show the effectiveness of the proposed control strategy, which provides significant results using the AB fractional derivative operator in the Caputo sense, comparing it with the classical integer one. The results show the importance of choosing very well the fractional characterization of the order of the operators.</p>

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