Inverse problems for a multi-term time fractional evolution equation with an involution

This paper focuses on considering two inverse source problems (ISPs) for a multi-term time-fractional evolution equation with an involution term, interpolating the heat and wave equations. The fractional derivatives are defined in Caputo's sense. ISPs proved to be ill-posed sense of Hadamard. Recovering space dependent term from over-specified data given at some time constitute first ISP, while second ISP determination component is considered when condition integral type given. solution constructed by using Fourier's method. time-dependent components solutions presented terms multinomial Mittag-Leffler function. Under certain conditions, shown classical solutions. In addition, particular examples formulated illustrate obtained results ISPs.