Results 11 to 20 of about 126,725,776 (290)

Fractional Telegraph Equation with the Caputo Derivative

Fractal and Fractional, 2023
The Cauchy problem for the telegraph equation (Dtρ)2u(t)+2αDtρu(t)+Au(t)=f(t) (0<t≤T,0<ρ<1, α>0), with the Caputo derivative is considered. Here, A is a selfadjoint positive operator, acting in a Hilbert space, H; Dt is the Caputo fractional derivative.
Ravshan Ashurov, Rajapboy Saparbayev
core   +5 more sources

Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions

Journal of Function Spaces, 2021
In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and strongly m-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities ...
Xue Feng, Baolin Feng, Ghulam Farid, Sidra Bibi, Qi Xiaoyan, Ze Wu   +5 more
doaj   +2 more sources

The general Caputo–Katugampola fractional derivative and numerical approach for solving the fractional differential equations

Alexandria Engineering Journal
In this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the ψ-Caputo–Katugampola fractional derivative (ψ-CKFD).
Lakhlifa Sadek, Sahar Ahmed ldris, Fahd Jarad   +2 more
doaj   +2 more sources

Incomplete Caputo fractional derivative operators

Advances in Difference Equations, 2018
The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types of incomplete hypergeometric functions and obtain their integral ...
Mehmet Ali Özarslan, Ceren Ustaoglu
doaj   +2 more sources

Caputo and Atangana-Baleanu-Caputo Fractional Derivative Applied to Garden Equation

Turkish Journal of Science, 2020
In this study, the garden equation which is a nonlinear partial differential equation is discussed. First, we will expand the garden equation to the Caputo derivative and Atangana-Baleanu fractional derivative in the sense of Caputo. Then, we will then demonstrate the existence of the new equation with the help of the fixed point theorem.
Mustafa Ali Dokuyucu
openaire   +3 more sources

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

On Riemann‐Liouville and Caputo Derivatives [PDF]

Discrete Dynamics in Nature and Society, 2011
Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann‐Liouville (RL) derivative, one of mostly used fractional derivatives.
Changpin Li, Deliang Qian, YangQuan Chen
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Numerical solutions of fractional optimal control with Caputo–Katugampola derivative

Advances in Difference Equations, 2021
In this paper, we present a numerical technique for solving fractional optimal control problems with a fractional derivative called Caputo–Katugampola derivative. This derivative is a generalization of the Caputo fractional derivative.
N. H. Sweilam, A. M. Nagy, T. M. Al-Ajami   +2 more
doaj   +1 more source

Generalized Proportional Caputo Fractional Differential Equations with Noninstantaneous Impulses: Concepts, Integral Representations, and Ulam-Type Stability

Mathematics, 2022
The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physics ...
Ravi Agarwal, Snezhana Hristova, Donal O’Regan   +2 more
doaj   +1 more source

Properties of the Caputo-Fabrizio Fractional Derivative [PDF]

, 2020
In this paper, we investigate some properties related Caputo-Fabrizio (CF) fractional derivative. We prove some regularity properties and bounds characterizing the Caputo-Fabrizio derivative operator.
D. Lau-Alfonso, L., Rodr ́ıguez Ricard, M., A. Mboro Nchama, G., M. Leo ́n Mec ́ıas, A.   +3 more
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