A Note on Fractional Differential Subordination Based on the Srivastava-Owa Fractional Operator

(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.

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Applications of differential Subordination and Superordination Involving Certain Fractional Operator

Current Topics on Mathematics and Computer Science Vol. 1 ◽

10.9734/bpi/ctmcs/v1/9050d ◽

2021 ◽

pp. 7-16

Author(s):

Jamal Salah

Keyword(s):

Differential Subordination ◽

Fractional Operator ◽

Differential Subordination And Superordination

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The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

Demonstratio Mathematica ◽

10.1515/dema-2019-0017 ◽

2019 ◽

Vol 52 (1) ◽

pp. 204-212 ◽

Cited By ~ 3

Author(s):

Fuat Usta ◽

Mehmet Zeki Sarıkaya

Keyword(s):

Differential Equations ◽

Fractional Integral ◽

Existence Of Solutions ◽

Integral Inequalities ◽

Fractional Operator ◽

Van Der Pol ◽

Global Existence Of Solutions ◽

Explicit Bounds ◽

Fractional Differential ◽

Conformable Fractional Integral

AbstractIn this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.

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Constrained Controllability of theh-Difference Fractional Control Systems with Caputo Type Operator

Discrete Dynamics in Nature and Society ◽

10.1155/2015/638420 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Ewa Pawluszewicz

Keyword(s):

Sufficient Conditions ◽

Fractional Operator ◽

Discrete Time System ◽

Time System ◽

Fractional Systems ◽

Constrained Controllability ◽

Fractional Differential ◽

Target Set ◽

Fractional Control ◽

Necessary And Sufficient

The problem of controllability to a given convex target set of linear fractional systems withh-difference fractional operator of Caputo type is studied. Necessary and sufficient conditions of controllability with constrained controllers for such systems are given. Problem of approximation of a continuous-time system with Caputo fractional differential by a discrete-time system withh-difference fractional operator of Caputo type is discussed.

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On a Fractional Operator Combining Proportional and Classical Differintegrals

Mathematics ◽

10.3390/math8030360 ◽

2020 ◽

Vol 8 (3) ◽

pp. 360 ◽

Cited By ~ 33

Author(s):

Dumitru Baleanu ◽

Arran Fernandez ◽

Ali Akgül

Keyword(s):

Integral Operator ◽

Differential Equations ◽

Fractional Derivative ◽

Fractional Differential Equations ◽

Fractional Integral ◽

Inverse Operator ◽

Fractional Operator ◽

Special Cases ◽

Non Local ◽

Fractional Differential

The Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviours by fractional differential equations. It is defined, for a differentiable function f ( t ) , by a fractional integral operator applied to the derivative f ′ ( t ) . We define a new fractional operator by substituting for this f ′ ( t ) a more general proportional derivative. This new operator can also be written as a Riemann–Liouville integral of a proportional derivative, or in some important special cases as a linear combination of a Riemann–Liouville integral and a Caputo derivative. We then conduct some analysis of the new definition: constructing its inverse operator and Laplace transform, solving some fractional differential equations using it, and linking it with a recently described bivariate Mittag-Leffler function.

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Certain new weighted estimates proposing generalized proportional fractional operator in another sense

Advances in Difference Equations ◽

10.1186/s13662-020-02935-z ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 1

Author(s):

Thabet Abdeljawad ◽

Saima Rashid ◽

A. A. El-Deeb ◽

Zakia Hammouch ◽

Yu-Ming Chu

Keyword(s):

Integral Operator ◽

Fractional Integral ◽

Mathematical Physics ◽

Fractional Integral Operator ◽

Fractional Operator ◽

Weighted Estimates ◽

Fractional Differential ◽

Positive Functions ◽

Katugampola Fractional Integral ◽

Hadamard Fractional Integral

Abstract The present work investigates the applicability and effectiveness of generalized proportional fractional integral ($\mathcal{GPFI}$ GPFI ) operator in another sense. We aim to derive novel weighted generalizations involving a family of positive functions n ($n\in \mathbb{N}$ n ∈ N ) for this recently proposed operator. As applications of this operator, we can generate notable outcomes for Riemann–Liouville ($\mathcal{RL}$ RL ) fractional, generalized $\mathcal{RL}$ RL -fractional operator, conformable fractional operator, Katugampola fractional integral operator, and Hadamard fractional integral operator by changing the domain. The proposed strategy is vivid, explicit, and it can be used to derive new solutions for various fractional differential equations applied in mathematical physics. Certain remarkable consequences of the main theorems are also figured.

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Synchronization via Fractal-Fractional Differential Operators On Two-Mass Torsional Vibration System Consisting of Motor and Roller

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4052189 ◽

2021 ◽

Author(s):

Kashif Ali Abro ◽

A A

Keyword(s):

Torsional Vibration ◽

Electromechanical Coupling ◽

Differential Operators ◽

Electrical Equipment ◽

Fractional Operator ◽

Vibration System ◽

Numerical Schemes ◽

Fractional Differential ◽

Differential Scheme ◽

Fractional Differential Operators

Abstract Due to increasing demand of lightweight shafts from industries, the drive systems are crucially demanded for larger inertias of motors and load machines because of control structures for the electrical equipment. The mathematical modeling of two-mass torsional vibration system consisting of motor and roller has been proposed via newly presented fractal-fractional differential operators. The dynamical model of the electromechanical coupling main drive system of rolling mill is based on total kinetic energy and potential energy on the basis of two degree-of-freedom. The fractal and fractional evolutionary differential equation containing nonlinearity have been investigated for the derivation of numerical schemes. Three types of numerical schemes say Caputo differential scheme, Caputo-Fabrizio differential scheme and Atangana-Baleanu differential scheme have been established through Adams-Bashforth-Moulton method. In order to check the stability and effectiveness, we presented the chaotic comparison of Caputo fractal-fractional operator, Caputo-Fabrizio fractal-fractional operator and Atangana fractal-fractional operator on the basis of dynamical embedded parameters (vibration angle, rotational speed, stiffness coefficient, load friction damping torque and few others).

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Some fractional differential equations involving generalized hypergeometric functions

Journal of Applied Analysis ◽

10.1515/jaa-2019-0004 ◽

2019 ◽

Vol 25 (1) ◽

pp. 37-44 ◽

Cited By ~ 3

Author(s):

Praveen Agarwal ◽

Feng Qi ◽

Mehar Chand ◽

Gurmej Singh

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Hypergeometric Functions ◽

Integral Transforms ◽

Fractional Operator ◽

Generalized Hypergeometric Functions ◽

Fractional Differential

Abstract In the paper, using the generalized Marichev–Saigo–Maeda fractional operator, the authors establish some fractional differential equations associated with generalized hypergeometric functions and, by employing integral transforms, present some image formulas of the resulting equations.

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On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator

Advances in Difference Equations ◽

10.1186/s13662-021-03459-w ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Maryam Aleem ◽

Mujeeb Ur Rehman ◽

Jehad Alzabut ◽

Sina Etemad ◽

Shahram Rezapour

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Continuous Dependence ◽

Existence Results ◽

Existence Theory ◽

Fractional Operator ◽

General Boundary Conditions ◽

Special Cases ◽

Fractional Differential ◽

Continuous Dependence Of Solutions

AbstractIn this work, we study the existence, uniqueness, and continuous dependence of solutions for a class of fractional differential equations by using a generalized Riesz fractional operator. One can view the results of this work as a refinement for the existence theory of fractional differential equations with Riemann–Liouville, Caputo, and classical Riesz derivative. Some special cases can be derived to obtain corresponding existence results for fractional differential equations. We provide an illustrated example for the unique solution of our main result.

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Image Enhancement Based on Fractional Differential and Image Entropy

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.159.232 ◽

2010 ◽

Vol 159 ◽

pp. 232-235

Author(s):

Ya Wei Liu ◽

Jian Wei Li

Keyword(s):

Mutual Information ◽

Image Enhancement ◽

Experimental Results ◽

Fractional Operator ◽

Selection Differential ◽

Image Entropy ◽

Enhancement Method ◽

Fractional Differential ◽

The Difference

In this paper, a new image enhancement method is proposed based on fractional differential, which can select the differential order automatically by the difference of mutual information (DMI). DMI describes the increase of mutual information in original and enhancement image. Being a measure of ascertaining the ehancement effect, it is considered getting the information balance in the images processed by different differential order. According to it, a criterion of selection differential order is put forward. Image convolutions are implemented with fractional operator in different scales, and then DMI of adjacent scales are calculated. The differential order can be selected in which the DMI is the mininum. The experimental results indicate that the proposed method is effective, and has better result compared with other methods.

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