Existence and multiplicity of solutions to an ab- stract Cauchy problem for an evolution equation involving fractional dissipation term of Caputo type - HOUARI, Nourredine; GEORGIEV, Svetlin Georgiev; HALLOUZ, Abdelhamid; BRAIKI, Hocine Mohamed (Studia Universitatis Babeș-Bolyai Mathematica, 2025)
The aim of this work is to investigate the existence and multiplicity of solutions to a nonhomogenious quasi-linear second order evolution equation involving a fractional dissipation term of Caputo type in abstract framework. Some criteria on the existence of at least one or two solutions are obtained by using some well-known fixed-point theorems for the sum of two operators. An example is presented to validate our analysis. Mathematics Subject Classification (2010): 35J15, 35J25, 93B24, 26A33. Received 05 May 2025; Accepted 21 July 2025.