Weak almost periodic and optimal mild solutions of fractional evolution equations.
Weak solution for fractional order integral equations in reflexive Banach spaces
Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces.
Weak solutions to differential equations with left and right fractional derivatives defined on
Weighted endpoint estimates for commutators of fractional integrals
Given , , and , we give sufficient conditions on weights for the commutator of the fractional integral operator, , to satisfy weighted endpoint inequalities on and on bounded domains. These results extend our earlier work [3], where we considered unweighted inequalities on .
Weighted function spaces of fractional derivatives for vector fields.
Weighted modular inequalities for Hardy-type operators on monotone functions.
Weighted norm inequalities for parabolic fractional integrals
Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω
Mathematics Subject Classification: 26A16, 26A33, 46E15.There are known various statements on weighted action of one-dimensional and multidimensional fractional integration operators in spaces of continuous functions, such as weighted generalized Hölder spaces Hω0(ρ) of functions with a given dominant ω of their continuity modulus.
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 ...
Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations
Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12In 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...