Dear all,
I have developed a new technique which solves linear integro-differential equations of fractional type. This includes Fredholm and Volterra equations.
I am looking for an application which can be modeled into such equation so I can apply my method. It can be any kind of application.
I also solve mixed system of equations e.g.1. A system of multiple Fredholm equations of different order of fractional derivatives (0, 1/2, 1, 3/2, etc..) or e.g. 2. A system of same or different kinds of Volterra equations. So, if there is an application to this kind of equation, it would be great!
I would appreciate your help. Please refer me to an article.
P.S. Only linear equations please.
Thank you very much in advance.
Sarah
You can use it to model physical systems which are characterised by Levy jumps. It can also be used to solve fractional-Schrodinger equation for quantum systems. See, https://arxiv.org/abs/1604.02550
Also use it to model Time Fractional Heat Equation. Find the article in Google Scholar: Solution of Fractional Volterra Integral Equation and Non-Homogeneous Time Fractional Heat Equation using Integral Transform of Pathway Type by Agarwal
Good afternoon! Look at Warburg admittance https://en.wikipedia.org/wiki/Warburg_element
The current J throught it connected with exitation voltage V as J=d1/2/dt1/2V. It is possible to construct more complex admittances.
Dear Sara,
First of all, let me congratulate you for your achievement.
Do not bother about applications. Go on your research,
But if you want to have an application, you can see
http://www.sciencedirect.com/science/article/pii/S037704271000066X
thank you my friend Luis - Felipe Velázquez - León , you are always present.
Best regards.
A fractional Integro-Differential equation arises in modeling processes in applied sciences (Physics, Engineering, Finance, Biology …). Many problems in Viscoelasticity, Acoustics, Electromagnetics, Hydrology and other areas of application can be modeled by fractional Integro-Differential equations.
I hope you can get use of the following paper;
Article Approximate Solution of Fractional Integro-Differential Equa...
Best regards
Sarmad.
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