scholarly journals Analytical solution of non-linear fractional Burger’s equation in the framework of different fractional derivative operators

2020 ◽  
Vol 19 ◽  
pp. 103397 ◽  
Author(s):  
Igor Malyk ◽  
Mansour Mohammed A. Shrahili ◽  
Ahmed Roby Shafay ◽  
Pranay Goswami ◽  
Shivani Sharma ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Non Linear ◽  
Fractional Derivative Operators

scholarly journals Analytical solution for non-linear local fractional Bratu-type equation in a fractal space

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 3941-3947
Author(s):  
Shao-Wen Yao ◽  
Wen-Jie Li ◽  
Kang-Le Wang
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Variational Formulation ◽  
Decomposition Method ◽  
Approximate Analytical Solution ◽  
Type Equation ◽  
Transform Method ◽  
Inverse Transform ◽  
Non Linear ◽  
Fractal Space

In this paper, the non-linear local fractional Bratu-type equation is described by the local fractional derivative in a fractal space, and its variational formulation is successfully established according to semi-inverse transform method. Finally, we find the approximate analytical solution of the local fractional Bratu-type equation by using Adomina decomposition method.

Time–Space Fractional Burger's Equation on Time Scales

2017 ◽  
Vol 12 (3) ◽  
Author(s):  
A. Neamaty ◽  
M. Nategh ◽  
B. Agheli
Keyword(s):  
Fractional Derivative ◽  
Traffic Flow ◽  
Time Scales ◽  
Flow Problem ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Time Space ◽  
Indefinite Integral ◽  
A Chain ◽  
The Given

This paper deals with a newly born fractional derivative and integral on time scales. A chain rule is derived, and the given indefinite integral is being discussed. Also, an application to the traffic flow problem with a fractional Burger's equation is presented.

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.

Sign in / Sign up

Export Citation Format

Share Document