**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**861

# Search results for: Saigo's generalized fractional calculus

##### 861 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

##### 860 Fractional Calculus into Structural Dynamics

**Authors:**
Jorge Lopez

**Abstract:**

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

##### 859 Modified Fractional Curl Operator

**Authors:**
Rawhy Ismail

**Abstract:**

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

##### 858 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

##### 857 B Spline Finite Element Method for Drifted Space Fractional Tempered Diffusion Equation

**Authors:**
Ayan Chakraborty,
BV. Rathish Kumar

**Abstract:**

**Keywords:**
B-spline finite element,
error estimates,
Gronwall's lemma,
stability,
tempered fractional

##### 856 A Mathematical Model Approach Regarding the Children’s Height Development with Fractional Calculus

**Authors:**
Nisa Özge Önal,
Kamil Karaçuha,
Göksu Hazar Erdinç,
Banu Bahar Karaçuha,
Ertuğrul Karaçuha

**Abstract:**

**Keywords:**
children growth percentile,
children physical development,
fractional calculus,
linear and polynomial model

##### 855 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

##### 854 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

##### 853 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

##### 852 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

##### 851 Nonlocal Phenomena in Quantum Mechanics

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

**Abstract:**

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

##### 850 Numerical Solution of Magneto-Hydrodynamic Flow of a Viscous Fluid in the Presence of Nanoparticles with Fractional Derivatives through a Cylindrical Tube

**Authors:**
Muhammad Abdullah,
Asma Rashid Butt,
Nauman Raza

**Abstract:**

**Keywords:**
viscous fluid,
magnetic particles,
fractional calculus,
laplace transformation

##### 849 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

##### 848 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

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

**Authors:**
Marcin Sowa

**Abstract:**

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

##### 846 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

##### 845 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

##### 844 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

##### 843 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

##### 842 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

##### 841 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

##### 840 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

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

**Authors:**
Lev Idels,
Arcady Ponosov

**Abstract:**

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

##### 838 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

##### 837 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

##### 836 Mixed Sub-Fractional Brownian Motion

**Authors:**
Mounir Zili

**Abstract:**

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

##### 835 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

##### 834 Mixed-Sub Fractional Brownian Motion

**Authors:**
Mounir Zili

**Abstract:**

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

##### 833 Stability Analysis of Tumor-Immune Fractional Order Model

**Authors:**
Sadia Arshad,
Yifa Tang,
Dumitru Baleanu

**Abstract:**

**Keywords:**
cancer model,
fractional calculus,
numerical simulations,
stability analysis

##### 832 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