abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions which contain some positive constants.

We discuss integral estimates for domain of solutions to some canonical Riccati and Sturm–Liouville equations on the line. The approach is applied to Hardy and Poincaré type inequalities with weights.

We present a new Liouville-integrable natural Hamiltonian system on the (cotangent bundle of the) sphere S2. The second integral is cubic in the momenta. MSC2000: 37J35, 58F07, 58F17, 70H06, 70E40

The authors shall discuss Heinz inequalities involving Riemann-Liouville fractional integrals for certain unitarily invariant norms. By using the convexity of function and fractional Hermit-Hadamard integral inequality, some refinements of Heinz inequalities are derived.

and Applied Analysis 3 is called the Riemann-Liouville fractional integral of h of order α > 0 when the right side exists. Here Γ is the usual Gamma function