Aydin, MustafaMahmudov, Nazim I.2025-05-102025-05-1020240239-75282300-191710.24425/bpasts.2024.1491702-s2.0-85186755999https://doi.org/10.24425/bpasts.2024.149170https://hdl.handle.net/20.500.14720/11064Aydin, Mustafa/0000-0003-0132-9636We introduce the Sobolev-type multi -term mu-fractional evolution with generalized fractional orders with respect to another function. We make some applications of the generalized Laplace transform. In the sequel, we propose a novel type of Mittag-Leffler function generated by noncommutative linear bounded operators with respect to the given function and give a few of its properties. We look for the mild solution formula of the Sobolev-type evolution equation by building on the aforementioned Mittag-Leffler-type function with the aid of two different approaches. We share new special cases of the obtained findings.eninfo:eu-repo/semantics/openAccessDegenerate Evolution EquationSobolevGeneralized Laplace TransformFractional Derivative With Respect To Another FunctionMittag-Leffler Type FunctionArticle722Q4Q3WOS:001183748800008