Role of fractal–fractional derivative on ferromagnetic fluid via fractal Laplace transform: A first problem via fractal–fractional differential operator

2021 ◽  
Vol 85 ◽  
pp. 76-81 ◽  
Author(s):  
Kashif Ali Abro
Keyword(s):  
Differential Operator ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Ferromagnetic Fluid

scholarly journals On Caputo modification of Hadamard-type fractional derivative and fractional Taylor series

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Rashida Zafar ◽  
Mujeeb ur Rehman ◽  
Moniba Shams
Keyword(s):  
Differential Operator ◽  
Fractional Derivative ◽  
Taylor Series ◽  
General Framework ◽  
Taylor Expansion ◽  
Fractional Integral ◽  
Haar Wavelet ◽  
Wavelet Method ◽  
Fractional Differential Operator ◽  
Fractional Differential

Abstract In this paper a general framework is presented on some operational properties of Caputo modification of Hadamard-type fractional differential operator along with a new algorithm proposed for approximation of Hadamard-type fractional integral using Haar wavelet method. Moreover, a generalized Taylor expansion based on Caputo–Hadamard-type fractional differential operator is also established, and an example is presented for illustration.

scholarly journals Second Hankel Determinant for a Class of Analytic Functions Defined by Fractional Derivative

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
A. K. Mishra ◽  
P. Gochhayat
Keyword(s):  
Differential Operator ◽  
Fractional Derivative ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Integral Transform ◽  
Hankel Determinant ◽  
Nonlinear Functional ◽  
Fractional Differential Operator ◽  
Second Hankel Determinant ◽  
Fractional Differential

By making use of the fractional differential operatorΩzλdue to Owa and Srivastava, a class of analytic functionsℛλ(α,ρ)    (0≤ρ≤1,  0≤λ<1,    |α|<π/2)is introduced. The sharp bound for the nonlinear functional|a2a4−a32|is found. Several basic properties such as inclusion, subordination, integral transform, Hadamard product are also studied.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

scholarly journals On Multivalent Analytic Functions Considered by a Multi-Arbitrary Differential Operator in a Complex Domain

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 315
Author(s):  
Najla M. Alarifi ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Integral Operators ◽  
Upper And Lower Bounds ◽  
Fractional Operator ◽  
Convolution Operators ◽  
Linear Convolution ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Special Case

(1) Background: There is an increasing amount of information in complex domains, which necessitates the development of various kinds of operators, such as differential, integral, and linear convolution operators. Few investigations of the fractional differential and integral operators of a complex variable have been undertaken. (2) Methods: In this effort, we aim to present a generalization of a class of analytic functions based on a complex fractional differential operator. This class is defined by utilizing the subordination and superordination theory. (3) Results: We illustrate different fractional inequalities of starlike and convex formulas. Moreover, we discuss the main conditions to obtain sandwich inequalities involving the fractional operator. (4) Conclusion: We indicate that the suggested class is a generalization of recent works and can be applied to discuss the upper and lower bounds of a special case of fractional differential equations.

Symmetry analysis of the generalized space and time fractional Korteweg–de Vries equation

2021 ◽  
Author(s):  
Jian-Gen Liu ◽  
Xiao-Jun Yang ◽  
Yi-Ying Feng ◽  
Lu-Lu Geng
Keyword(s):  
Fractional Derivative ◽  
Kdv Equation ◽  
Symmetry Analysis ◽  
Analysis Method ◽  
Space And Time ◽  
Fractional Differential Operator ◽  
Time Differential ◽  
De Vries ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

In this paper, we studied the generalized space and time fractional Korteweg–de Vries (KdV) equation in the sense of the Riemann–Liouville fractional derivative. Initially, the symmetry of this considered equation through the symmetry analysis method was obtained. Next, a one-parameter Lie group of point transformation was yielded. Then, this considered fractional model can be translated into an ordinary differential equation of fractional order via the Erdélyi–Kober fractional differential operator and the Erdélyi–Kober fractional integral operator. Finally, with the help of the nonlinear self-adjointness, conservation laws of the generalized space and time fractional KdV equation can be found. This approach can provide us with a new scheme for studying space and time differential equations of fractional derivative.

scholarly journals One-Phase Problems for Discontinuous Heat Transfer in Fractal Media

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Dumitru Baleanu ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Differential Operator ◽  
Transient Heat Transfer ◽  
Fractal Models ◽  
Fractal Media ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
The One

We first propose the fractal models for the one-phase problems of discontinuous transient heat transfer. The models are taken in sense of local fractional differential operator and used to describe the (dimensionless) melting of fractal solid semi-infinite materials initially at their melt temperatures.

Lie symmetries analysis and conservation laws for the fractional Calogero–Degasperis–Ibragimov–Shabat equation

2018 ◽  
Vol 15 (07) ◽  
pp. 1850110 ◽  
Author(s):  
S. Sahoo ◽  
S. Saha Ray
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Operator ◽  
Conservation Laws ◽  
Symmetry Analysis ◽  
Lie Symmetries ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Conservation Theorem

The present paper includes the study of symmetry analysis and conservation laws of the time-fractional Calogero–Degasperis–Ibragimov–Shabat (CDIS) equation. The Erdélyi–Kober fractional differential operator has been used here for reduction of time fractional CDIS equation into fractional ordinary differential equation. Also, the new conservation theorem has been used for the analysis of the conservation laws. Furthermore, the new conserved vectors have been constructed for time fractional CDIS equation by means of the new conservation theorem with formal Lagrangian.

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