**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2438

# Search results for: modified Riemann-Liouville fractional derivative

##### 2438 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

##### 2437 Hypergeometric Solutions to Linear Nonhomogeneous Fractional Equations with Spherical Bessel Functions of the First Kind

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

**Abstract:**

**Keywords:**
caputo fractional derivatives,
hypergeometric functions,
linear differential equations,
spherical Bessel functions

##### 2436 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

##### 2435 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

##### 2434 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

##### 2433 Modified Fractional Curl Operator

**Authors:**
Rawhy Ismail

**Abstract:**

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

##### 2432 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

##### 2431 Modeling the Compound Interest Dynamics Using Fractional Differential Equations

**Authors:**
Muath Awadalla,
Maen Awadallah

**Abstract:**

**Keywords:**
compound interest,
fractional differential equation,
hadamard fractional derivative,
optimization

##### 2430 Nonlocal Phenomena in Quantum Mechanics

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

**Abstract:**

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

##### 2429 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

##### 2428 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

##### 2427 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

##### 2426 Application of a SubIval Numerical Solver for Fractional Circuits

**Authors:**
Marcin Sowa

**Abstract:**

**Keywords:**
numerical method,
SubIval,
fractional calculus,
numerical solver,
circuit analysis

##### 2425 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

##### 2424 Optimization of Coefficients of Fractional Order Proportional-Integrator-Derivative Controller on Permanent Magnet Synchronous Motors Using Particle Swarm Optimization

**Authors:**
Ali Motalebi Saraji,
Reza Zarei Lamuki

**Abstract:**

**Keywords:**
speed control loop of permanent magnet synchronous motor,
fractional and full order proportional-integrator-derivative controller,
coefficients optimization,
particle swarm optimization,
improvement of behavior

##### 2423 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

##### 2422 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

##### 2421 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

##### 2420 An Antibacterial Dental Restorative Containing 3,4-Dichlorocrotonolactone: Synthesis, Formulation and Evaluation

**Authors:**
Dong Xie,
Leah Howard,
Yiming Weng

**Abstract:**

**Keywords:**
antibacterial,
dental restorative,
compressive strength,
S. mutans viability

##### 2419 Fractional Calculus into Structural Dynamics

**Authors:**
Jorge Lopez

**Abstract:**

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

##### 2418 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

##### 2417 A Coupled System of Caputo-Type Katugampola Fractional Differential Equations with Integral Boundary Conditions

**Authors:**
Yacine Arioua

**Abstract:**

**Keywords:**
fractional differential equations,
coupled system,
Caputo-Katugampola derivative,
fixed point theorems,
existence,
uniqueness

##### 2416 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

##### 2415 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

##### 2414 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

##### 2413 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

##### 2412 Weak Solutions Of Stochastic Fractional Differential Equations

**Authors:**
Lev Idels,
Arcady Ponosov

**Abstract:**

**Keywords:**
delay equations,
operator methods,
stochastic noise,
weak solutions

##### 2411 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

##### 2410 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

##### 2409 Mixed Sub-Fractional Brownian Motion

**Authors:**
Mounir Zili

**Abstract:**

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