How to create custom forms to filter views results in Drupalgap
You could first create a custom form: http://docs.drupalgap.org/7/Forms/Creating_a_Custom_Form

Then in its submit handler build a Views Render Array and inject it into a waiting div placeholder element (markup widget) on the form:

http://docs.drupalgap.org/7/Views/Displaying_a_View/Views_Render_Array
http://docs.drupalgap.org/7/Forms/Form_Elements/Element_Markup

Or have the submit handler go to a page with arguments: http://docs.drupalgap.org/7/Pages/Page_Arguments

Then that's page's page_callback could build a Views Render Array and use the search string as a contextual filter to the View.