scholarly journals DGJ Method for Linear and Nonlinear Third order Fractional Differential Equation

2018 ◽  
Author(s):  
Mahmut Modanli
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Fractional Differential Equation ◽  
Initial Boundary ◽  
Third Order ◽  
Partial Differential ◽  
Approximation Solution ◽  
The Third ◽  
Numerical Result ◽  
Fractional Differential

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

scholarly journals Initial boundary value problems for a fractional differential equation with hyper-Bessel operator

2018 ◽  
Vol 21 (1) ◽  
pp. 200-219 ◽  
Author(s):  
Fatma Al-Musalhi ◽  
Nasser Al-Salti ◽  
Erkinjon Karimov
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Initial Boundary ◽  
Fractional Diffusion ◽  
Initial Boundary Value Problems ◽  
Bessel Differential Operator ◽  
Fractional Differential ◽  
Inverse Source Problems ◽  
Initial Boundary Value

AbstractDirect and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.

scholarly journals The Exact Iterative Solution of Fractional Differential Equation with Nonlocal Boundary Value Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Jinxiu Mao ◽  
Zengqin Zhao ◽  
Chenguang Wang
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Fractional Differential Equation ◽  
Nonlocal Boundary ◽  
Approximation Error ◽  
Iterative Solution ◽  
Stieltjes Integral ◽  
Iterative Technique ◽  
Integral Conditions ◽  
Fractional Differential

We deal with a singular nonlocal fractional differential equation with Riemann-Stieltjes integral conditions. The exact iterative solution is established under the iterative technique. The iterative sequences have been proved to converge uniformly to the exact solution, and estimation of the approximation error and the convergence rate have been derived. An example is also given to demonstrate the results.

scholarly journals I. On curvature and orthogonal surfaces

1873 ◽  
Vol 21 (139-147) ◽  
pp. 166-167
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Orthogonal System ◽  
The Other ◽  
Third Order ◽  
Partial Differential ◽  
The Third ◽  
The Subject

The principal object of the present Memoir is the establishment of the partial differential equation of the third order satisfied by the parameter of a family of surfaces belonging to a triple orthogonal system. It was first remarked by Bouquet that a given family of surfaces does not in general belong to an orthogonal system, but that (in order to its doing so) a condition must be satisfied: it was afterwards shown by Serret that the condition is that the parameter considered as a function of the coordinates must satisfy a partial differential equation of the third older, this equation was not obtained by him or the other French geometers engaged on the subject, although methods of obtaining it, essentially equivalent but differing in form, were given by Darboux and Levy.

scholarly journals Exact Solutions of Bernoulli and Logistic Fractional Differential Equations with Power Law Coefficients

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2231
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Power Law ◽  
Dynamic Processes ◽  
Nonlinear Fractional Differential Equation ◽  
First Order ◽  
Fractional Differential ◽  
Special Case

In this paper, we consider a nonlinear fractional differential equation. This equation takes the form of the Bernoulli differential equation, where we use the Caputo fractional derivative of non-integer order instead of the first-order derivative. The paper proposes an exact solution for this equation, in which coefficients are power law functions. We also give conditions for the existence of the exact solution for this non-linear fractional differential equation. The exact solution of the fractional logistic differential equation with power law coefficients is also proposed as a special case of the proposed solution for the Bernoulli fractional differential equation. Some applications of the Bernoulli fractional differential equation to describe dynamic processes with power law memory in physics and economics are suggested.

scholarly journals Using matrix stability for variable telegraph partial differential equation

2020 ◽  
Vol 10 (2) ◽  
pp. 237-243
Author(s):  
Mahmut Modanli ◽  
Bawar Mohammed Faraj ◽  
Faraedoon Waly Ahmed
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Initial Boundary ◽  
Difference Schemes ◽  
Constant Time ◽  
Partial Differential ◽  
Approximation Solution ◽  
Euler Formula ◽  
Time Space ◽  
Matrix Stability

The variable telegraph partial differential equation depend on initial boundary value problem has been studied. The coefficient constant time-space telegraph partial differential equation is obtained from the variable telegraph partial differential equation throughout using Cauchy-Euler formula. The first and second order difference schemes were constructed for both of coefficient constant time-space and variable time-space telegraph partial differential equation. Matrix stability method is used to prove stability of difference schemes for the variable and coefficient telegraph partial differential equation. The variable telegraph partial differential equation and the constant coefficient time-space telegraph partial differential equation are compared with the exact solution. Finally, approximation solution  has been found for both equations. The error analysis table presents the obtained numerical results.

scholarly journals Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation

2021 ◽  
Vol 11 (03) ◽  
pp. 189-206
Author(s):  
Zaki Mrzog Alaofi ◽  
Talaat Sayed Ali ◽  
Faisal Abd Alaal ◽  
Silvestru Sever Dragomir
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Polynomial Spline ◽  
Third Order ◽  
Partial Differential ◽  
The Third
Sign in / Sign up

Export Citation Format

Share Document