Some generalized fractional calculus operators and their applications in integral equations

OP Agrawal - Fractional Calculus and Applied Analysis, 2012 - Springer
In this paper, we survey some generalizations of fractional integrals and derivatives and
present some of their properties. Using these properties, we show that many integral …

Concept of dynamic memory in economics

VV Tarasova, VE Tarasov - … in Nonlinear Science and Numerical Simulation, 2018 - Elsevier
In this paper we discuss a concept of dynamic memory and an application of fractional
calculus to describe the dynamic memory. The concept of memory is considered from the …

A Caputo fractional derivative of a function with respect to another function

R Almeida - Communications in Nonlinear Science and Numerical …, 2017 - Elsevier
In this paper we consider a Caputo type fractional derivative with respect to another function.
Some properties, like the semigroup law, a relationship between the fractional derivative …

Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications

R Almeida, AB Malinowska… - … Methods in the Applied …, 2018 - Wiley Online Library
This paper is devoted to the study of the initial value problem of nonlinear fractional
differential equations involving a Caputo‐type fractional derivative with respect to another …

[PDF][PDF] Fractional Differentiation Inequalities

GA Anastassiou - 2009 - dspace.kottakkalfarookcollege.edu …
In 1991, although I had graduated in 1984, my great Ph. D. thesis advisor JHB Kemperman
recommended that I read the very interesting paper of J. Canavati [101], having to do with …

Macroeconomic models with long dynamic memory: Fractional calculus approach

VE Tarasov, VV Tarasova - Applied Mathematics and Computation, 2018 - Elsevier
This article discusses macroeconomic models, which take into account effects of power-law
fading memory. The power-law long memory is described by using the mathematical tool of …

A brief story about the operators of the generalized fractional calculus

V Kiryakova - Fractional Calculus and Applied Analysis, 2008 - eudml.org
Abstract top 2000 Mathematics Subject Classification: 26A33, 33C60, 44A20In this survey
we present a brief history and the basic ideas of the generalized fractional calculus (GFC) …

FMNSICS: Fractional Meyer neuro-swarm intelligent computing solver for nonlinear fractional Lane–Emden systems

Z Sabir, MAZ Raja, M Umar, M Shoaib… - Neural Computing and …, 2022 - Springer
The fractional neuro-evolution-based intelligent computing has substantial potential to solve
fractional order systems represented with Lane–Emden equation arising in astrophysics …

A fractional derivative with two singular kernels and application to a heat conduction problem

D Baleanu, M Jleli, S Kumar, B Samet - Advances in Difference Equations, 2020 - Springer
In this article, we suggest a new notion of fractional derivative involving two singular kernels.
Some properties related to this new operator are established and some examples are …

Fractional derivatives and the fundamental theorem of fractional calculus

Y Luchko - Fractional Calculus and Applied Analysis, 2020 - degruyter.com
In this paper, we address the one-parameter families of the fractional integrals and
derivatives defined on a finite interval. First we remind the reader of the known fact that …