On the convolution equations over the quarter-plane.
Numerical solution of initial and singularly perturbed two-point boundary value problems using adaptive spline function approximation.
A first order accuracy scheme on non-uniform mesh.
Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s
Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05. We give the proofs of the existence and regularity of the solutions in the space C^∞ (t > 0;H^(s+2) (R^n)) ∩ C^0(t ≧ 0;H^s(R^n)); s ∊ R, for the 1-term, 2-term,..., n-term time-fractional equation evaluated from the time fractional equation of distributed order with spatial Laplace operator Δx ...
Fractional Derivatives in Spaces of Generalized Functions
MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo We generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of distributions....
Page 1