Does Fortran have undefined behavior?
Yes, it has. It is just called differently. There are many things that you could do and will make your code not standard conforming, for which there is no requirement to for the processor (compiler) to diagnose such non-conformance (of course, many deviations must be diagnosed). Often the situations will be similar to C undefined-behaviour one (like accesing an array out-of-bounds, signed integer overflow,...). We just say that the code is not standard conforming, that means the standard does not prescribe the outcome of such a code. Such code is not covered but the standard and so anything can result if some compiler (processor) does compile it and you do run it.
That is different from processor dependent behaviour, that one is standard and just implementation dependent.
Just searching here at StackOverflow should give you plenty of examples. Like Is passing the same entity to arguments with different intent undefined behavior? How do Fortran and MPI_Reduce deal with integer overflow?
This answer just answers the question asked but does not attempt to list all possible kinds of UB that can happen in Fortran.
The Fortran standard does admit similar concepts to the idea of "undefined behaviour" of C and C++. It's often phrased by people supporting broken Fortran code as "the compiler may now start World War III", or similar.
The Fortran language specification has two ideas of conformance (see Fortran 2018, 4.2). The main one is what a program must look like to be able to considered a Fortran program. The second is what a processor must do in response to a submitted program unit to be considered a Fortran processor.
If a conforming Fortran processor is asked to process something that is not a Fortran program, the standard rarely says what must happen. There are some diagnoses that must be offered, but often there is not.
In the case of "using a variable after its deallocation", an attempt to do this is a violation of that part of the language standard that defines the Fortran program. A compiler may then "start World War III" without violating the Fortran standard, because the Fortran standard doesn't say that it must not (or must do something else).
Now, how do we look at the Fortran standard document and decide whether the not-quite-Fortran program has a particular required effect? The text from 4.2 mentions a number of situations where a compiler must have "the capability to detect and report the use within a submitted program unit". If your proposed program doesn't hit any of those you're in "undefined" territory.
The main time a program error must be reportable is in the case
the use within a submitted program unit of a form or relationship that is not permitted by the numbered syntax rules or constraints
Let's consider arbitrarily Fortran 2018, 15.5.1C1523 (R1520) Syntax of a procedure reference. We see things like "R1520":
R1520 function-reference is procedure-designator ( [ actual-arg-spec-list ] )
and "C1523":
C1523 (R1520) The procedure-designator shall designate a function.
before we have a list of things like:
The data-ref in a procedure-designator shall not be an unallocated allocatable variable or a pointer that is not associated.
In this case, the rule R1520, numbered constraint C1523 (which applies to this rule) and following text give constraints on the Fortran program. If your submitted program doesn't meet those, it's not a conforming Fortran program.
A compiler asked to process such a non-conforming program, where that program violates R1520 or C1523, must be able to detect that (based on the above). A compiler doesn't have to complain about or detect violations of the un-numbered text. It's allowed to assume that any program it's presented with doesn't break such an un-numbered restriction.
This one here I quote is (coincidentally) one example of a prohibition on a program incorrectly using a previously deallocated variable.
If a processor operates in a "compile-then-run" way, the numbered rules/constraints are typically ones that can be assessed "at compile time".
Another specific and significant example of undefined behaviour is using a variable without first giving it a value ("defining" it). The Fortran standard simply says (Fortran 2018 9.2 p2):
A reference is permitted only if the variable is defined. A reference to a data pointer is permitted only if the pointer is associated with a target object that is defined. A variable becomes defined with a value when events described in 19.6.5 occur.
This isn't a numbered syntax rule or constraint and is a (significant) burden on the program that the compiler is allowed to assume has been met.