This paper inspects the existence of the regular temporal source term in the fractional diffusion-wave equation. Addressing a complex inverse problem involving time fractional Caputo derivative and a non-local damping term  featuring  two parameter Mittag-Leffler type function. Mathematical challenge arises due to presence of convolution term and a set of Samarskii-Ionkin boundary conditions. To validate the solution's existence, we establish estimates for infinite series involving the convolution of a three parameter Mittag-Leffler function. Our research contributes valuable insights at the intersection of mathematical analysis and fractional calculus providing a robust foundation for understanding and solving complex problems in this domain.