"Petitionary prayer" refers to a form of prayer where someone asks or requests something from a higher power or deity. It involves making specific requests or seeking help for oneself or others during a prayer. Full definition
Unhappily, a good deal of petitionary prayer as well as intercession seems to be based on the «magical» premise rather than the «religious» one. (religion-online.org)
Clearly, our uncertainty about petitionary prayer reflects our uncertainty about how God governs the world. (religion-online.org)
(See, for example, Gerald Heard, A Preface to Prayer, in which prayer is distinguished as low, middle, and high, low prayer being petitionary prayer for oneself, middle prayer petition for others, and high prayer the prayer of «simple attention.») (religion-online.org)