The main objective of this paper is to use the generalized proportional Hadamard fractional integral operator establish some new inequalities for extended Chebyshev functionals. In addition, we investigate positive continuous functions by employing a operator. findings study are theoretical but have potential help solve additional practical problems in mathematical physics, statistics, and appr...

In this work we study the finite difference method for fractional diffusion equation with high-dimensional hyper-singular integral Laplacian. We first propose a simple and easy-to-implement discrete approximation, i.e., centered scheme γth-order (γ≤2) convergence operator. Based on established then construct to solve equations analyze stability in energy norm (0<α≤2) maximum (1<α≤2). further pr...

2 Young’s integrals and stochastic differential equations driven by fractional Brownian motions 4 2.1 Young’s integral and basic estimates . . . . . . . . . . . . . . . . . . 4 2.2 Stochastic differential equations driven by a Hölder path . . . . . . . 7 2.3 Multidimensional extension . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Fractional calculus . . . . . . . . . . . . . . . . . . . ...

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.