*MOST* alarm systems run on 12V power and are usually designed to run from a SLA backup battery if mains power is interrupted. Replace the main panel or control unit's backup battery with an external 12V deep cycle lead acid (leisure) battery with enough capacity for at least a week's operation in a tamper-proof battery box, add enough solar panel area to keep the battery charged in the month with the least insolation + a charge controller so it doesn't overcharge and fake out the mains power detection circuit* so the alarm panel doesn't complain about mains failure and you'll have a fully functional alarm system that can use any sensors, sounders and accessories that don't require their own separate mains supply. Many systems can either have their own GSM dialer board fitted or can power and trigger an external third party GSM dialer.
Don't buy any systems or accessories that don't either come with or have a publicly available installers manual complete with the default system codes if applicable - the security alarm industry can be a bit of an old boys club (not as bad as the HVAC industry) and some manufacturers can be rather unhelpful to DIYers.
* that's where you need someone with enough electronics knowledge and test equipment to determine if its just a matter of tying the MCU's sensing input to a logic level or whether it needs to be fed a regular mains frequency pulse + build a micropower circuit to fake it.