Pseudo-Differential Equations Cauchy Problem Caputo Fractional Derivative Mittag-Leffler Function Inhomogeneous Equation Time-Fractional Equation 26A33 45K05 35A05 35S10 35S15 33E12
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 9, No 1, (2006), 01p-16p
In the present paper the Cauchy problem for partial inhomogeneous pseudo-differential equations of fractional order is analyzed. The solvability theorem for the Cauchy problem in the space ΨG,2(R^n) of functions in L2(R^n) whose Fourier transforms are compactly supported in a domain G ⊆ R^n is proved. The representation of the solution in terms of pseudo-differential operators is given. The solvability theorem in the Sobolev spaces H^s,2(R^n), s ∈ R^1 is also established.