These are Highly non-linear second order partial differential equations
and it is not easy to obtain exact solutions of these equations.
One-dimensional DTM can be extended (Chen and Ho, 1999) into two-dimensional DTM for resolving the integral and differential equations
On the other hand, impulsive differential equations
are often used for description some processes or system with impulsive effects, impulsive (partial) differential equations
with Caputo fractional derivative were widely studied in [21-32], and the existence of solutions was considered for impulsive differential equations
with Hadamard fractional derivative in .
A kind of functional differential equations
of third order with retarded argument has been considered.
During the last few years, the numerical methods and exact solution methods have been proposed to solve fractional differential equations
, for example, the Adomian decomposition method , the homotopy perturbation method [11, 12], the variational iteration method [13, 14], the differential transform method [15,16], the G'/G method [17, 18], the first integral method , and the exp-function method .
In dynamic systems modeling, particular rules of mass and energy conservation are used, mathematically expressed as balance equations, that are simply differential equations
, where derivation variable is time, t, or with partial derivates--where there is at least one derivation variable besides time (a space coordinate as example).
Rezapour: Some existence results on nonlinear fractional differential equations
Typically, Fourier, Laplace, ELzaki and Sumudu transforms are the convenient mathematical tools for solving differential equations
In the late eighteen century Sophus Lie made use of transformation groups in an effort to bring the results of Evarist Galois on polinomial equations to the differential equations
The study of fuzzy differential equations
(FDEs) forms a suitable setting for the mathematical modelling of real world problems in which uncertainty or vagueness pervades.
of fractional order have recently proved valuable tools in the modelling of many physical phenomena [5; 13; 14; 25; 26].
Abstract: We conclude this section some applications of first order differential equations
The problem of existence of solutions of Cauchy-type problems for ordinary differential equations
of fractional order in spaces of integrable functions was studied in numerous works [17, 27], a similar problem in spaces of continuous functions was studied in .
It lists additional mathematical models based on partial differential equations
and shows how the methods of separation of variables and eigenfunction expansion work for equations other than heat, wave, and Laplace.
Fazal Mahmood Mahomed, here Tuesday delivered a series of lectures on Historical Aspects of Differential Equations
and Idea of Symmetry to MS/PHD students in the department of mathematics at International Islamic University (IIU).