**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**16954

# Search results for: fractional order systems

##### 16954 Design Fractional-Order Terminal Sliding Mode Control for Synchronization of a Class of Fractional-Order Chaotic Systems with Uncertainty and External Disturbances

**Authors:**
Shabnam Pashaei,
Mohammadali Badamchizadeh

**Abstract:**

**Keywords:**
terminal sliding mode control,
fractional-order calculus,
chaotic systems,
synchronization

##### 16953 Fractional Order Differentiator Using Chebyshev Polynomials

**Authors:**
Koushlendra Kumar Singh,
Manish Kumar Bajpai,
Rajesh Kumar Pandey

**Abstract:**

**Keywords:**
fractional order derivative,
chebyshev
polynomials,
signals,
S-G differentiator

##### 16952 Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems

**Authors:**
Kazem Ghanbari,
Yousef Gholami

**Abstract:**

**Keywords:**
fractional derivatives and integrals,
Hamiltonian system,
Lyapunov-type inequalities,
stability,
disconjugacy

##### 16951 Observer-Based Leader-Following Consensus of Nonlinear Fractional-Order Multi-Agent Systems

**Authors:**
Ali Afaghi,
Sehraneh Ghaemi

**Abstract:**

**Keywords:**
fractional-order multi-agent systems,
leader-following consensus,
nonlinear dynamics,
directed graphs

##### 16950 Backstepping Design and Fractional Differential Equation of Chaotic System

**Authors:**
Ayub Khan,
Net Ram Garg,
Geeta Jain

**Abstract:**

**Keywords:**
backstepping method,
fractional order,
synchronization,
chaotic system

##### 16949 Application of Fractional Model Predictive Control to Thermal System

**Authors:**
Aymen Rhouma,
Khaled Hcheichi,
Sami Hafsi

**Abstract:**

*.*

**Keywords:**
fractional model predictive control,
fractional order systems,
thermal system,
predictive control

##### 16948 Caputo-Type Fuzzy Fractional Riccati Differential Equations with Fuzzy Initial Conditions

**Authors:**
Trilok Mathur,
Shivi Agarwal

**Abstract:**

**Keywords:**
Caputo-type fuzzy fractional derivative,
Fractional Riccati differential equations,
Laplace-Adomian-Pade method,
Mittag Leffler function

##### 16947 Fractional Order Sallen-Key Filters

**Authors:**
Ahmed Soltan,
Ahmed G. Radwan,
Ahmed M. Soliman

**Abstract:**

**Keywords:**
Sallen-Key,
fractance,
stability,
low-pass filter,
analog filter

##### 16946 Numerical Solutions of Fractional Order Epidemic Model

**Authors:**
Sadia Arshad,
Ayesha Sohail,
Sana Javed,
Khadija Maqbool,
Salma Kanwal

**Abstract:**

**Keywords:**
Fractional diﬀerential equation,
Numerical simulations,
epidemic model,
transmission dynamics

##### 16945 Derivation of Fractional Black-Scholes Equations Driven by Fractional G-Brownian Motion and Their Application in European Option Pricing

**Authors:**
Changhong Guo,
Shaomei Fang,
Yong He

**Abstract:**

**Keywords:**
European option pricing,
fractional Black-Scholes equations,
fractional g-Brownian motion,
Taylor's series of fractional order,
uncertain volatility

##### 16944 Fractional Calculus into Structural Dynamics

**Authors:**
Jorge Lopez

**Abstract:**

**Keywords:**
coupled oscillators,
fractional calculus,
fractional oscillator,
structural dynamics

##### 16943 Numerical Solution of Space Fractional Order Solute Transport System

**Authors:**
Shubham Jaiswal

**Abstract:**

**Keywords:**
spatial fractional order advection-dispersion equation,
second-kind shifted Chebyshev polynomial,
collocation method,
conservative system,
non-conservative system

##### 16942 Nonlocal Phenomena in Quantum Mechanics

**Authors:**
Kazim G. Atman,
Hüseyin Sirin

**Abstract:**

**Keywords:**
Einstein’s Coefficients,
Fractional Calculus,
Fractional Quantum Mechanics,
Nonlocal Theories

##### 16941 Analytical Solutions of Time Space Fractional, Advection-Dispersion and Whitham-Broer-Kaup Equations

**Authors:**
Muhammad Danish Khan,
Imran Naeem,
Mudassar Imran

**Abstract:**

**Keywords:**
modified Riemann-Liouville fractional derivative,
lie-symmetries,
optimal system,
invariant solutions

##### 16940 Melnikov Analysis for the Chaos of the Nonlocal Nanobeam Resting on Fractional-Order Softening Nonlinear Viscoelastic Foundations

**Authors:**
Guy Joseph Eyebe,
Gambo Betchewe,
Alidou Mohamadou,
Timoleon Crepin Kofane

**Abstract:**

**Keywords:**
chaos,
fractional-order,
Melnikov method,
nanobeam

##### 16939 An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon

**Authors:**
Haniye Dehestani,
Yadollah Ordokhani

**Abstract:**

**Keywords:**
collocation method,
fractional partial differential equations,
legendre-laguerre functions,
pseudo-operational matrix of integration

##### 16938 A Dynamical Study of Fractional Order Obesity Model by a Combined Legendre Wavelet Method

**Authors:**
Hakiki Kheira,
Belhamiti Omar

**Abstract:**

**Keywords:**
Caputo derivative,
epidemiology,
Legendre wavelet method,
obesity

##### 16937 Fractional-Order PI Controller Tuning Rules for Cascade Control System

**Authors:**
Truong Nguyen Luan Vu,
Le Hieu Giang,
Le Linh

**Abstract:**

**Keywords:**
Bode’s ideal transfer function,
fractional calculus,
fractional–order proportional integral (FOPI) controller,
cascade control system

##### 16936 Global Mittag-Leffler Stability of Fractional-Order Bidirectional Associative Memory Neural Network with Discrete and Distributed Transmission Delays

**Authors:**
Swati Tyagi,
Syed Abbas

**Abstract:**

**Keywords:**
bidirectional associative memory neural network,
existence and uniqueness,
fractional-order,
Lyapunov function,
Mittag-Leffler stability

##### 16935 Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems

**Authors:**
Ali Dorostkar

**Abstract:**

**Keywords:**
tangent line,
fractional dimension,
root,
optimization problem

##### 16934 Modified Fractional Curl Operator

**Authors:**
Rawhy Ismail

**Abstract:**

**Keywords:**
curl operator,
fractional calculus,
fractional curl operators,
Maxwell equations

##### 16933 Solutions of Fractional Reaction-Diffusion Equations Used to Model the Growth and Spreading of Biological Species

**Authors:**
Kamel Al-Khaled

**Abstract:**

**Keywords:**
fractional partial differential equations,
reaction-diﬀusion equations,
adomian decomposition,
biological species

##### 16932 Anisotropic Total Fractional Order Variation Model in Seismic Data Denoising

**Authors:**
Jianwei Ma,
Diriba Gemechu

**Abstract:**

**Keywords:**
anisotropic total fractional order variation,
fractional order bounded variation,
seismic random noise attenuation,
split Bregman algorithm

##### 16931 Numerical Solution of Space Fractional Order Linear/Nonlinear Reaction-Advection Diffusion Equation Using Jacobi Polynomial

**Authors:**
Shubham Jaiswal

**Abstract:**

**Keywords:**
space fractional order linear/nonlinear reaction-advection diffusion equation,
shifted Jacobi polynomials,
operational matrix,
collocation method,
Caputo derivative

##### 16930 Fundamental Solutions for Discrete Dynamical Systems Involving the Fractional Laplacian

**Authors:**
Jorge Gonzalez Camus,
Valentin Keyantuo,
Mahamadi Warma

**Abstract:**

**Keywords:**
discrete fractional Laplacian,
explicit representation of solutions,
fractional heat and wave equations,
fundamental

##### 16929 Analytical Design of Fractional-Order PI Controller for Decoupling Control System

**Authors:**
Truong Nguyen Luan Vu,
Le Hieu Giang,
Le Linh

**Abstract:**

**Keywords:**
ideal transfer function of bode,
fractional calculus,
fractional order proportional integral (FOPI) controller,
decoupling control system

##### 16928 Dynamical Analysis of the Fractional-Order Mathematical Model of Hashimoto’s Thyroiditis

**Authors:**
Neelam Singha

**Abstract:**

**Keywords:**
adomian decomposition method,
fractional derivatives,
Hashimoto's thyroiditis,
mathematical modeling

##### 16927 Nonhomogeneous Linear Fractional Differential Equations Will Bessel Functions of the First Kind Giving Hypergeometric Functions Solutions

**Authors:**
Fernando Maass,
Pablo Martin,
Jorge Olivares

**Abstract:**

**Keywords:**
Caputo,
fractional calculation,
hypergeometric,
linear differential equations

##### 16926 Multiloop Fractional Order PID Controller Tuned Using Cuckoo Algorithm for Two Interacting Conical Tank Process

**Authors:**
U. Sabura Banu,
S. K. Lakshmanaprabu

**Abstract:**

**Keywords:**
Cuckoo algorithm,
mutliloop fractional order PID controller,
two Interacting conical tank process

##### 16925 Linear fractional differential equations for second kind modified Bessel functions

**Authors:**
Jorge Olivares,
Fernando Maass,
Pablo Martin

**Abstract:**

**Keywords:**
Caputo,
modified Bessel functions,
hypergeometric,
linear fractional differential equations,
transform Laplace