International Monthly Seminar on Time Scales Analysis #7

In this conversation, examines the long-term existence of solutions for a system of weakly coupled equations involving fractional evolution and various nonlinearities. The main focus is on analyzing the relationship between the regularity of initial data, memory terms, and the allowable range of exponents in a specific equation. Using L^p–L^q estimates for solutions of associated linear fractional $σ$-evolution equations with vanishing right-hand sides, along with a fixed-point method, the study establishes the existence of small-data solutions with in certain admissible exponent ranges.