BookDOI
Topics in fractional differential equations
TLDR
In this article, partial hyperbolic functional differential equations are used to express fractional order Riemann-Liouville integral functions, and implicit Partial Hyperbolic Functional Differential Equations.Abstract:
Preface.- 1. Preliminary Background.- 2. Partial Hyperbolic Functional Differential Equations.- 3. Partial Hyperbolic Functional Differential Inclusions.- 4. Impulsive Partial Hyperbolic Functional Differential Equations.- 5. Impulsive Partial Hyperbolic Functional Differential Inclusions.- 6. Implicit Partial Hyperbolic Functional Differential Equations.- 7. Fractional Order Riemann-Liouville Integral Equations.- References.- Index.read more
Citations
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Journal ArticleDOI
Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
TL;DR: Almeida et al. as mentioned in this paper used the CIDMA-Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia), within project UID/MAT/04106/2013.
Journal ArticleDOI
On development of fractional calculus during the last fifty years
TL;DR: The evolution of fractional calculus is addressed and an assertive measure of the research development is established.
Journal ArticleDOI
The Chronicles of Fractional Calculus
TL;DR: In this article, a survey analyzes and measures the evolution that occurred during the last five decades in the light of books, journals and conferences dedicated to the theory and applications of fractional calculus, dealing with operations of integration and differentiation of arbitrary (fractional) order and their generalizations.
Journal ArticleDOI
A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability
TL;DR: In this article, the existence of solutions and weak solutions for some classes of Hadamard and Hilfer fractional differential equations were proved by applying the fixed point theory, and the technique of strong and weak measures of noncompactness.
Journal ArticleDOI
Science metrics on fractional calculus development since 1966
TL;DR: In this paper, the evolution of fractional calculus has been analyzed and measured in the last fifty years, and a considerable progress has been made in the area of Fractional Calculus.
References
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Journal ArticleDOI
Recent history of fractional calculus
TL;DR: A survey of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date can be found in this article, where the authors report some of the most important documents and major events.
Journal ArticleDOI
Variable-order fractional differential operators in anomalous diffusion modeling
TL;DR: In this article, a classification of variable-order fractional diffusion models based on the possible physical origins which prompt the variable order is presented. But the characteristics of the new models change with time, space, concentration or other independent quantities.
Journal ArticleDOI
Mechanics with variable-order differential operators
TL;DR: This work presents the novel concept of Variable-Order (VO) Calculus through the description of a simple problem in Mechanics, and the VO-Calculus formulation is compared to a CO- Calculus model to show the limitations of the latter in resolving the transition between the relevant dynamic regimes.
Journal ArticleDOI
Fractional diffusion in inhomogeneous media
TL;DR: In this paper, the authors study the evolution of a composite system consisting of two separate regions with different sub-diffusion exponents and demonstrate the effects of non-trivial drift and subdiffusion whose laws are changed in the course of time.
Journal ArticleDOI
The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus
TL;DR: This paper is a short description of the recent results on an important class of the so-called ''Special Functions of Fractional Calculus'' (SF of FC), which became important as solutions of fractional order differential and integral equations, control systems and refined mathematical models of various physical, chemical, economical, management, bioengineering phenomena.