Fixed point theorem and iterated function system in φ-metric modular space

We introduce and study the concept of φ -metric modular space and, then define φ - α -Meir-Keeler contraction on it and explore its fixed point. Further, we define the Hausdorff distance between two non-empty compact subsets of the considered space. Some topological properties of φ -metric modular space are also explored. Additionally, we prove the existence of the attractor (fractal) of the IFS consisting of φ - α -Meir-Keeler contractions.