General fractional calculus and Prabhakar’s theory

Theory, Methods, and Applications of Fractional Calculus

1 Institute for Groundwater Studies, University of the Free State, Bloemfontein 9300, South Africa 2Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia 3 Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa 4Department of Mathematical Engineering, Yildiz Technical Univ...

Fractional Order Calculus in Control Theory

The main aim of this contribution is to introduce the fundamentals of the Fractional Order Calculus (FOC) and outline its possible application to analysis and synthesis of control systems. The basic theoretical concepts of FOC are followed by techniques for potential fractional order systems description and stability investigation. Moreover, the paper offers the overview of the existing fractio...

A Nonlinear Creep-damage Constitutive Model of Mudstone Based on the Fractional Calculus Theory

During the flood development in an oil field, the creep characteristic of mudstone is one of the important factors causing casing damage. In this study, based on the theory of fractional order differential and taking into account the creep damage evolution rules, a fractional nonlinear creep-damage model is proposed to reflect the instantaneous deformation in loading processes and the accelerat...

General Splay: A Basic Theory and Calculus

The directory problem, that of handling an on-line series of INSERT, DELETE and FIND requests, is for most applications addressed satisfactorily by balanced search trees (BST) (see e.g., [Ov83] for a trace of BST's from [AVL62] and on), which guarantee O(logN) worst time for each of these operations. For applications however in which the access frequencies are highly biased the " overbalancedne...

Analytic function theory, fractional calculus and their applications