Are virtual particles only a fictive tool in equations?

Virtual particles refer to actual, nonzero features in the quantum fields of real objects, but they are features that are not particles in many ways so you should not expect anything from their being named "particle".

Basically, the idea of virtual particles was invented as a device for when you want to hold on to the particle picture while doing quantum physics. Keep in mind, we know that actually nothing is really a particle, but rather quantum fields are the fundamental objects. We can derive particle-like motions in fields but fields also show other behaviours. If you insist on everything being somehow a particle then these other behaviours need to be recognised and treated with care. Someone decided they shall be called "virtual particles".

For example take a hydrogen atom, a bound proton and electron. There is for sure a real electromagnetic field inside the atom, holding it together. This electromagnetic field is certainly not a particle in any classical sense. With quantum fields we can choose to represent the electromagnetic field in terms of photons (i.e., using a photon-like basis of states to describe the field). But in doing so we see that the photons inside of a hydrogen atom are not like familiar radiating photons in free space but rather something else, virtual somehow.

Again, the only thing that is fundamental and real is the quantum field, which does not care about any distinctions we choose to make between real and virtual particles, or between particles and waves. Nevertheless we like to come up with funny names to help ourselves come to grips with the reality. But perhaps the term "virtual particle" is more misleading than it is helpful.

Virtual particles are not observable by definition. They represent "internal lines" in Feynman diagrams. For example, this diagram:

Here two electrons move toward each other, interact, then move away from each other. The external lines represent "real" electrons which we can measure/observe. The internal line here is an excitation of the electromagnetic field which we call a "virtual photon." Similarly, virtual electrons/quarks/gluons/etc. all correspond to internal lines in Feynman diagrams. So virtual particles are not observable by definition. If they were observable, they wouldn't be virtual.

The true mediators of forces are the quantum fields.

A thorough discussion of virtual particles and their properties (and possible way of existence) is given in the following two recent essays of mine:

The Physics of Virtual Particles

Misconceptions about Virtual Particles

From the introduction to the second essay:

''virtual particles are defined as (intuitive imagery for) internal lines in a Feynman diagram. Their name derives by analogy to the external lines, which may be linked to observable stable or unstable particles. The 4-momentum vector of a virtual particle has the physical meaning of an integration variable in the integral corresponding to the diagram, and takes all possible values, making it off-shell.

States involving virtual particles cannot be created since quantum field theory has creation operators only for observable particles whose 4-momentum satisfies the mass-shell constraint. For lack of a state, virtual particles have none of the usual physical characteristics of real particles: They cannot be said to exist in space and time, have no position, no meaningful probabilities to be created or destroyed anywhere, no life-time, cannot cause anything, interact with anything or affect anything. Therefore there is also no dynamics, speed of motion, or world lines. (In physics, dynamics is always tied to states and an equation of motion. Neither exists for virtual particles.) [...]

The only way the usual dynamical language for virtual particles is justified by the theory is as purely figurative analogy in ”virtual reality”, useful for informal talk about complicated formulas and for superficial summaries in lectures capturing the imagination of the audience.

This has to be kept in mind when reading in professional scientific publications statements involving virtual particles. Otherwise many statements become completely misleading, inviting a magical view of microphysics and weird speculation, without the slightest support in theory or experiment.''

This is just the tip of an iceberg....