On a new class of fractional operators
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In this paper, the authors introduce new fractional integration and differentiation operators based on the standard fractional calculus iteration procedure on conformable derivatives and define spaces and present some theorems related to these operators.Abstract:
This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.read more
Citations
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A new definition of fractional derivative
TL;DR: In this article, a new fractional derivative of the Caputo type is proposed and some basic properties are studied, such as adaptively changing the memory length, the new definition is capable of capturing local memory effect in a distinct way, which is critical in modelling complex systems where the short memory properties has to be considered.
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New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations
TL;DR: In this article, the authors considered integro-differential equations involving Atangana-Baleanu fractional derivatives which contain the generalized Mittag-Leffler functions in their kernels and examined the existence and uniqueness of solutions to such equations in Banach spaces.
Journal ArticleDOI
On Fractional Operators and Their Classifications
Dumitru Baleanu,Arran Fernandez +1 more
TL;DR: Fractional calculus dates its inception to a correspondence between Leibniz and L’Hopital in 1695 as discussed by the authors, and it has become a thriving field of research not only in mathematics but also in other parts of science such as physics, biology, and engineering.
Journal ArticleDOI
Fractional logistic models in the frame of fractional operators generated by conformable derivatives
TL;DR: In this article, the existence and uniqueness theorems to solutions of these models and discuss their stability by perturbing the equilibrium points are discussed and illustrated by illustrative numerical examples for the studied models.
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Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function
TL;DR: In this article, the generalized proportional fractional integral (GPF) integral is defined in the sense of another function and several inequalities for the GPF-integral with respect to another function are proved.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Book
Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
Journal ArticleDOI
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model
Abdon Atangana,Dumitru Baleanu +1 more
TL;DR: In this article, a new fractional derivative with non-local and no-singular kernel was proposed and applied to solve the fractional heat transfer model, and some useful properties of the new derivative were presented.