In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

We consider a Cauchy problem for the inhomogeneous differential equation given in terms of an unbounded linear operator A and Caputo fractional derivative order α∈(0,2) time. The previously known representation mild solution to such does not have conventional variation-of-constants like form, with propagator derived from associated homogeneous problem. Instead, it relies on existence two propag...

The goal of this work is to introduce the two-parameter conformable fractional semigroups and provide a definition its infinitesimal generator. For such generators, we develop multiple results. In addition, show that solution for abstract Cauchy problems.