Hello,
This is a common scenario of referencing missing assembly and instead a similar version one is found. Details and solution could be found at the following links:
The located assembly's manifest definition does not match the assembly reference
.Net picking wrong referenced assembly version

I am checking the progress of this issue. Please let me know if you have additional questions!

Hello, 

It is possible to use the existing 10.3 functionality together with the new product version you have purchased.

We have created version-free assemblies in order to make this possible. This will allow you to preserve the code and functionalities of the classic controls and still have the ability to add Aikido based controls respectively use the updated functionality for these. 

When your application is ready for publishing, remove the references to the DLLs with versioned assembly names and add references to the version-less assemblies. You may place the version-less DLLs in the bin folder of your application or in the GAC. 

The main idea behind using the version-free assemblies it to be able to use the Aikido based controls in projects using the older ones. This however does not mean they will provide additional/more functionality (or supported environment), than the existing in the classic controls assemblies.  

“As of the 2010.3 release, the version-less assemblies only support the DLLs to run the application. Should you need to open the application in Visual Studio ™ then you must revert the application to using versioned assembly names in order to get designer support. Once updates to the application are complete, you may configure the application to use the version-less assembly names once again before publishing.”

Please refer to our official online documentation/Application Maintenance: http://help.infragistics.com/Doc/ASPNET/?page=ASPNET_Versionless_Assemblies.html

To be able to use the designer you need to include the design assemblies in your project at design time. To use them you will either need to place them in the Bin folder or in a Design folder that is in the Bin folder. Here is a ref to the default location of the Version Free assemblies:
C:\Program Files (x86)\Infragistics\2013.2\ASP.NET\Version-Free.
These assemblies will have design in their name. To design properly you will need to have the design assembly that corresponds to the runtime assemblies you are using. For deploying your website you just have to deploy the assemblies to with your website either in the bin folder or the GAC. The design assemblies aren’t required for deployment.

You can go to the following link to see which assemblies are used with which controls.
http://help.infragistics.com/Doc/ASPNET/2013.2/CLR4.0/?page=Web_Assemblies.html 

Additional useful resource:
http://ko.infragistics.com/community/forums/t/73655.aspx