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In this article, Lie symmetry analysis is used to investigate invariance properties of some nonlinear fractional **partial** **differential** **equations** with conformable fractional time and space derivatives ... of Symmetry Methods to **Partial** **Differential** **Equations**. Springer, New York (2010)CrossRefGoogle Scholar
10.
Buckwar, E.; Luchko, Y.: Invariance of a **partial** **differential** equation of fractional order

The influence of certain discontinuous delays on the behavior of solutions to **partial** **differential** **equations** is studied. In Section 2, the initial value problems (IVP) are discussed for **differential**

IJMMS
LINEAR NEUTRAL **PARTIAL** **DIFFERENTIAL** **EQUATIONS**: A SEMIGROUP APPROACH
RAINER NAGEL
NGUYEN THIEU HUY
We study linear neutral PDEs of the form (?/?t)Fut = BFut + ?ut, t ? 0; u0(t) = ?(t), t ? 0 ... class of linear **partial** neutral functional-**differential** **equations** with nondense domain , J. **Differential** **Equations** 147 ( 1998 ), no. 2 , 285 - 332 .
[2] R. Datko , Linear autonomous neutral **differential**

This paper studies a class of high order delay **partial** **differential** **equations**. Employing high order delay **differential** inequalities, several oscillation criteria are established for such **equations** ... Journal of Applied Mathematics and Stochastic Analysis
OSCILLATION CRITERIA FOR HIGH ORDER DELAY **PARTIAL** **DIFFERENTIAL** **EQUATIONS** 1
0 University of Waterloo, Department of Applied Mathematics Waterloo

The aim of this paper is to study the numerical contour integral methods (NCIMs) for solving free-boundary **partial** **differential** **equations** (PDEs) from American volatility options pricing. Firstly, the ... **partial** **differential** **equations** (PDEs) from American volatility options written on the volatility whose price follows four well-known models: GBMP, MRGP, MRSRP, and MRLP. The original idea of NCIMs is

Some work is described and new topics are posed on initial and boundary-value problems for **partial** **differential** **equations** whose arguments have intervals of constancy. These **equations** are of ... defined as a continuous, sectionally smooth function that satisfies the equation
AND PHRASES; **Partial** **differential** **equations**; piecewise constant delay; boundary value problem; initial value problem

some quantity changes with some other quantity and its derivatives, there are more sophisticated **differential** **equations** known as **Partial** **Differential** **Equations** (PDEs), which describe how one quantity ... UNSOLVABLE LINEAR **PARTIAL**
**DIFFERENTIAL** **EQUATIONS** OF ORDER ONE
by Laura J. Fields
Departments of Mathematics and Physics
Fulbright College of Arts and Sciences
Faculty Mentor: Loredana Lanzani Department of

IJMMS
LINEAR NEUTRAL **PARTIAL** **DIFFERENTIAL** **EQUATIONS**: A SEMIGROUP APPROACH
RAINER NAGEL
NGUYEN THIEU HUY
We study linear neutral PDEs of the form (∂/∂t)Fut = BFut + Φut, t ≥ 0; u0(t) = ϕ(t), t ≤ 0 ... class of linear **partial** neutral functional-**differential** **equations** with nondense domain , J. **Differential** **Equations** 147 ( 1998 ), no. 2 , 285 - 332 .
[2] R. Datko , Linear autonomous neutral **differential**

The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic **partial** **differential** **equations** without use of linearizatlon techniques. We consider first a nonlinear ... International Journal of
APPLICATION OF DECOMPOSITION TO HYPERBOLIC 0
PARABOLIC 0
ELLIPTIC **PARTIAL** **DIFFERENTIAL** **EQUATIONS** 0
0 G. ADOMIAN Center for Applied Mathematics University of Georgia Athens

The influence of certain discontinuous delays on the behavior of solutions to some typical **equations** of mathematical physics is studied. ... successively to
construct the solution un (x,t) for any n > o. From (2.12) we conclude
that all un (x) satisfy (2.4?)
Differentiating (2.11) term by term
**PARTIAL** **DIFFERENTIAL** **EQUATIONS** WITH PIECEWIES CONSTANT

This paper studies a class of high order delay **partial** **differential** **equations**. Employing high order delay **differential** inequalities, several oscillation criteria are established for such **equations** ... Journal of Applied Mathematics and Stochastic Analysis
OSCILLATION CRITERIA FOR HIGH ORDER DELAY **PARTIAL** **DIFFERENTIAL** **EQUATIONS** 1
0 University of Waterloo, Department of Applied Mathematics Waterloo

Journal of
BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER **PARTIAL** **DIFFERENTIAL** **EQUATIONS** WITH OPERATOR COEFFICIENTS
KUDRATILLO S. FAYAZOV 0
EBERHARD SCHOCK 0
0 A(x , t )Lu(x, t )
Let T be some bounded ... -posed problems of the numerical theory and tomography , Siberian Math. J. 33 ( 1992 ), 27 - 41 .
[2] K. S. Fayazov and M. M. Lavrent 'ev, Cauchy problem for **partial** **differential** **equations** with operator

Some work is described and new topics are posed on initial and boundary-value problems for **partial** **differential** **equations** whose arguments have intervals of constancy. These **equations** are of ... defined as a continuous, sectionally smooth function that satisfies the equation
AND PHRASES; **Partial** **differential** **equations**; piecewise constant delay; boundary value problem; initial value problem

A historical development of the theory of linear **partial** **differential** equation is reviewed with comments. A recent development in the theory of linear **partial** **differential** **equations** is discussed. ... , Pseudo-**Differential** Operator, Elliptic **Differential**
1 Villa Orangini 119 Avenue de Braucolar Nice , France 06100
2 Linear **Partial** **Differential** **Equations** , Spectral Theory
3 Mathematics Department Carlton

This paper is devoted to closed-form solutions of the **partial** **differential** equation: θxx ... Internat. J. Math. & Math. Sci.
Vol.
ON CLOSED-FORM SOLUTIONS OF SOME NONLINEAR **PARTIAL** **DIFFERENTIAL** **EQUATIONS**
0 Okoya: Department of Mathematics, Obafemi Awolowo University , Ile-Ife, Nigeria E

, "Mathematical Modeling of the Fluorescence Recovery After Photobleaching (FRAP) Technique", is useful for courses related with the formulation and solution of mathematical models based on **partial** **differential**

The influence of certain discontinuous delays on the behavior of solutions to some typical **equations** of mathematical physics is studied. ... successively to
construct the solution un (x,t) for any n > o. From (2.12) we conclude
that all un (x) satisfy (2.4’)
Differentiating (2.11) term by term
**PARTIAL** **DIFFERENTIAL** **EQUATIONS** WITH PIECEWIES CONSTANT

linearization technique, which results in a robust method for solving nonlinear time-fractional **partial** **differential** **equations** on a bounded domain. Following the method detailed by Jacobs and Harley in [1, 2] we ... bounded domain. Other techniques such as the variational iteration method, Adomian decomposition method, and **differential** transform method have all been applied to fractional **partial** **differential** **equations**

other techniques without any conditions to apply on any system of **partial** **differential** **equations**.

We find maximum principles for solutions of semilinear elliptic **partial** **differential** **equations** of the forms: (1) Δ2u ... elliptic **partial** **differential** **equations** of the forms: (1) ? 2u+?f (u) = 0, ? ? R+ and (2) ? u + ?(? u)k + gu = 0, ? ? 0 in some region ? ? Rn. 1. Introduction. In [1], Chow and Dunninger proved the following