**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**185

# Search results for: fractional PDE

##### 185 Modified Fractional Curl Operator

**Authors:**
Rawhy Ismail

**Abstract:**

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

##### 184 Fractional Calculus into Structural Dynamics

**Authors:**
Jorge Lopez

**Abstract:**

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

##### 183 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

##### 182 Fractional Euler Method and Finite Difference Formula Using Conformable Fractional Derivative

**Authors:**
Ramzi B. Albadarneh

**Abstract:**

**Keywords:**
conformable fractional derivative,
finite difference formula,
fractional derivative,
finite difference formula

##### 181 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

##### 180 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

##### 179 Reduced Differential Transform Methods for Solving the Fractional Diffusion Equations

**Authors:**
Yildiray Keskin,
Omer Acan,
Murat Akkus

**Abstract:**

**Keywords:**
fractional diffusion equations,
Caputo fractional derivative,
reduced differential transform method,
partial

##### 178 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

##### 177 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

##### 176 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

##### 175 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

##### 174 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

##### 173 Oil Displacement by Water in Hauterivian Sandstone Reservoir of Kashkari Oil Field

**Authors:**
A. J. Nazari,
S. Honma

**Abstract:**

^{st}, and the relative permeability and fractional flow are analyzed. Steady state flow laboratory experiments are performed to empirically obtain the fractional flow curves and relative permeability in different water saturation ratio. The relative permeability represents the simultaneous flow behavior in the reservoir. The fractional flow approach describes the individual phases as fractional of the total flow. The fractional flow curve interprets oil displacement by water, and from the tangent of fractional flow curve can find out the average saturation behind the water front flow saturation. Therefore, relative permeability and fractional flow curves are suitable for describing the displacement of oil by water in a petroleum reservoir. The effects of irreducible water saturation, residual oil saturation on the displaceable amount of oil are investigated through Buckley-Leveret analysis.

**Keywords:**
fractional flow,
oil displacement,
relative permeability,
simultaneously flow

##### 172 Mixed Sub-Fractional Brownian Motion

**Authors:**
Mounir Zili

**Abstract:**

**Keywords:**
mixed Gaussian processes,
Sub-fractional Brownian motion,
sample paths

##### 171 Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation

**Authors:**
Sachin Kumar

**Abstract:**

**Keywords:**
fractional PDE,
fuzzy valued function,
diffusion equation,
Legendre polynomial,
spectral method

##### 170 Mixed-Sub Fractional Brownian Motion

**Authors:**
Mounir Zili

**Abstract:**

**Keywords:**
fractal dimensions,
mixed gaussian processes,
sample paths,
sub-fractional brownian motion

##### 169 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

##### 168 On the Fractional Integration of Generalized Mittag-Leffler Type Functions

**Authors:**
Christian Lavault

**Abstract:**

**Keywords:**
Fox–Wright Psi function,
generalized hypergeometric function,
generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators,
Saigo's generalized fractional calculus,
Sharma's M-series and K-function

##### 167 Effect of Fractional Flow Curves on the Heavy Oil and Light Oil Recoveries in Petroleum Reservoirs

**Authors:**
Abdul Jamil Nazari,
Shigeo Honma

**Abstract:**

**Keywords:**
fractional flow,
relative permeability,
oil recovery,
water fingering

##### 166 Extended Multi-Modulus Divider for Open Loop Fractional Dividers and Fractional Multiplying Delay Locked Loops

**Authors:**
Muhammad Swilam

**Abstract:**

**Keywords:**
extended multi-modulus divider (EMMD),
fractional multiplying delay locked loop,
open loop fractional divider,
sigma delta modulator

##### 165 Nonlocal Phenomena in Quantum Mechanics

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

**Abstract:**

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

##### 164 Cellular Automata Using Fractional Integral Model

**Authors:**
Yasser F. Hassan

**Abstract:**

**Keywords:**
fractional integral,
cellular automata,
memory,
learning

##### 163 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

##### 162 Multiple Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation

**Authors:**
A. Guezane-Lakoud,
S. Bensebaa

**Abstract:**

**Keywords:**
positive solution,
fractional caputo derivative,
Banach contraction principle,
Avery and Peterson fixed point theorem

##### 161 An Algorithm to Find Fractional Edge Domination Number and Upper Fractional Edge Domination Number of an Intuitionistic Fuzzy Graph

**Authors:**
Karunambigai Mevani Govindasamy,
Sathishkumar Ayyappan

**Abstract:**

**Keywords:**
fractional edge domination number,
intuitionistic fuzzy cycle,
intuitionistic fuzzy graph,
intuitionistic fuzzy path

##### 160 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

##### 159 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

##### 158 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

##### 157 Exactly Fractional Solutions of Nonlinear Lattice Equation via Some Fractional Transformations

**Authors:**
A. Zerarka,
W. Djoudi

**Abstract:**

**Keywords:**
fractional transformations,
nonlinear equation,
travelling wave solutions,
lattice equation

##### 156 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