Results 41 to 50 of about 1,913,284 (306)

Fractional Order Barbalat’s Lemma and its Applications in the Stability of Fractional Order Nonlinear Systems

Mathematical Modelling and Analysis, 2017
This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first.
Fei Wang, Yongqing Yang
doaj   +1 more source

An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative

Journal of Function Spaces, 2021
In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative.
H. R. Marasi, A. Soltani Joujehi, H. Aydi   +2 more
doaj   +1 more source

A generalization of truncated M-fractional derivative and applications to fractional differential equations

Applied Mathematics and Nonlinear Sciences, 2020
In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter ...
Esin İlhana, İ. O. Kıymazb, Esin Ilhan   +2 more
semanticscholar   +1 more source

On the Fractional Derivative of Dirac Delta Function and Its Application

Advances in Mathematical Physics, 2020
The Dirac delta function and its integer-order derivative are widely used to solve integer-order differential/integral equation and integer-order system in related fields. On the other hand, the fractional-order system gets more and more attention.
Zaiyong Feng, Linghua Ye, Yi Zhang
doaj   +1 more source

The dynamical analysis of a Tumor Growth model under the effect of fractal fractional Caputo-Fabrizio derivative

International Journal of Mathematics and Computer in Engineering, 2023
Fractal-fractional derivatives, which are still rather new, are frequently used to look into the complexities of an issue. Today, tumors are a prevalent and difficult-to-treat condition.
Rakhi Singh, Jyoti Mishra, V. Gupta
semanticscholar   +1 more source

Fuzzy Generalized Conformable Fractional Derivative

Advances in Fuzzy Systems, 2020
We give a new definition of fuzzy fractional derivative called fuzzy conformable fractional derivative. Using this definition, we prove some results and we introduce new definition of generalized fuzzy conformable fractional derivative.
Atimad Harir, Said Melliani, Lalla Saadia Chadli   +2 more
doaj   +1 more source

Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform

Fractal and Fractional, 2023
In this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived.
Ved Prakash Dubey, Jagdev Singh, Sarvesh Dubey, Devendra Kumar   +3 more
doaj   +1 more source

CAUCHY FRACTIONAL DERIVATIVE

Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics", 2020
In this paper, we introduce a new sort of fractional derivative. For this, we consider the Cauchy's integral formula for derivatives and modify it by using Laplace transform. So, we obtain the fractional derivative formula F(α)(s) = L{(–1)(α)L–1{F(s)}}. Also, we find a relation between Weyl's fractional derivative and the formula above.
openaire   +4 more sources

Comparative study of integer-order and fractional-order artificial neural networks: Application for mathematical function generation

e-Prime: Advances in Electrical Engineering, Electronics and Energy
This paper investigates the impact of fractional derivatives on the activation functions of an artificial neural network (ANN). Based on the results and analysis, a three-layer backpropagation neural network model with fractional and integer derivatives ...
Manisha Premkumar Joshi, Savita Bhosale, Vishwesh A. Vyawahare   +2 more
doaj   +1 more source

An analytical solution for the Caputo type generalized fractional evolution equation

Alexandria Engineering Journal, 2022
The Caputo type generalized fractional evolution equation is studied in this paper. Since the Caputo type generalized fractional derivative is well-known for being the generalization of Caputo fractional derivatives, this article’s studies contribute to ...
Wannika Sawangtong, Panumart Sawangtong
doaj   +1 more source