Fractional differential inclusions in the Almgren senseFractional Calculus and Applied Analysis - Tập 18 Số 3 - Trang 673-686 - 2015
Graef, John R., Henderson, Johnny, Ouahab, Abdelghani
In this paper we study fractional differential inclusions in the sense of Almgren. We begin with a discussion of multiple-valued functions in the Almgren sense and include the basic results needed to make the paper selfcontained. Sufficient background on the fractional calculus is provided to make the material accessible also to the non-specialist readers. Our main result gives sufficient conditio...... hiện toàn bộ
Trace Inequalities for Fractional Integrals in Mixed Norm Grand Lebesgue SpacesFractional Calculus and Applied Analysis - Tập 23 - Trang 1452-1471 - 2020
Vakhtang Kokilashvili, Alexander Meskhi
D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneou...... hiện toàn bộ
Sum of series and new relations for Mittag-Leffler functionsFractional Calculus and Applied Analysis - - 2024
Sarah A. Deif, E. Capelas de Oliveira
An integral equation is constructed relating the three-parameter Mittag-Leffler function with a perturbed one, from which a new property is derived. The latter helps in finding new sums of series of Mittag-Leffler functions. Also, a bound is obtained for the Mittag-Leffler function, allowing to perform a sensitivity analysis, being vital in the solution of fractional differential equations. The bo...... hiện toàn bộ
Covariant fractional extension of the modified Laplace-operator used in 3D-shape recoveryFractional Calculus and Applied Analysis - Tập 15 - Trang 332-343 - 2012
Richard Herrmann
Extending the Liouville-Caputo definition of a fractional derivative to a nonlocal covariant generalization of arbitrary bound operators acting on multidimensional Riemannian spaces an appropriate approach for the 3D shape recovery of aperture afflicted 2D slide sequences is proposed. We demonstrate, that the step from a local to a nonlocal algorithm yields an order of magnitude in accuracy and by...... hiện toàn bộ
Representation of holomorphic functions by schlömilch’s seriesFractional Calculus and Applied Analysis - Tập 16 - Trang 431-435 - 2013
Peter Rusev
A necessary and sufficient condition is given for holomorphic functions to be represented by series of the kind
$\sum\limits_{n = 0}^\infty {a_n J_0 (nz),z,a_n \in \mathbb{C},} $
where J
0(z) is the Bessel function of first kind with zero index. To derive the result, we use an Erdélyi-K...... hiện toàn bộ
Maximum Principles for a Class of Generalized Time-Fractional Diffusion EquationsFractional Calculus and Applied Analysis - Tập 23 Số 3 - Trang 822-836 - 2020
Zeng, Shengda, Migórski, Stanisław, Van Nguyen, Thien, Bai, Yunru
Two significant inequalities for generalized time fractional derivatives at extreme points are obtained. Then, we apply the inequalities to establish the maximum principles for multi-term time-space fractional variable-order operators. Finally, we employ the principles to investigate two kinds of diffusion equations involving generalized time-fractional Caputo derivatives and space-fractional Ries...... hiện toàn bộ