A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces

On The Sobolev-type Inequality for Lebesgue Spaces with a Variable Exponent

A numerical approach for variable-order fractional unified chaotic systems with time-delay

This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To ill...

Expression of the Lebesgue ∆-integral on time scales as a usual Lebesgue integral; application to the calculus of ∆-antiderivatives

The theory of dynamic equations appears in the literature in 1988 in the Ph. D. of S. Hilger [18]. The aim of this theory consists in to study differential and difference equations under the same formulation. Thus, the concepts of ∆– derivative and ∆−integral have been defined. These two concepts cover both the classical derivative and the Riemann integral together with the forward and sum oper...

Fractional Integration Operator of Variable Order in the Holder Spaces

The fractional integrals I+(x)0 of variable order e(x) are considered. A theorem on mapping properties of Ia+ in Holder-type spaces H is proved, this being a generalization of the well known Hardy-Li ttlewood theorem. KEYWORDSFractional integration, variable fractional order, mapping properties, Holder continuous functions, Hardy-Littlewood theorem. 1991 AHS SUBJECT CLASSIFICATION CODES. 26 A33...

The Sampling Theorem in Variable Lebesgue Spaces

hold. The facts above are well-known as the classical Shannon sampling theorem initially proved by Ogura [10]. Ashino and Mandai [1] generalized the sampling theorem in Lebesgue spaces L0(R) for 1 < p0 < ∞. Their generalized sampling theorem is the following. Theorem 1.1 ([1]). Let r > 0 and 1 < p0 < ∞. Then for all f ∈ L 0(R) with supp f̂ ⊂ [−rπ, rπ], we have the norm inequality C p r ‖f‖Lp0(Rn...