Analysis and numerical computations of the fractional regularized long‐wave equation with damping term
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6343
Abstract: This study explores the fractional damped generalized regularized long‐wave equation in the sense of Caputo, Atangana‐Baleanu, and Caputo‐Fabrizio fractional derivatives. With the aid of fixed‐point theorem in the Atangana‐Baleanu fractional derivative with Mittag‐Leffler–type kernel, we… read more here.
Keywords: wave equation; long wave; regularized long; atangana baleanu ... See more keywords
New discretization of Caputo–Fabrizio derivative
Sign Up to like & getrecommendations! Published in 2018 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-017-0514-1
Abstract: We derive a numerical approximation, namely L1–2 formula, to the Caputo–Fabrizio derivative by using a quadratic interpolation. Quadratic and cubic convergence rates are achieved for L1 and L1–2 formulas using Lagrange interpolation, respectively. We compute… read more here.
Keywords: caputo; caputo fabrizio; new discretization; discretization caputo ... See more keywords
Hilfer–Katugampola fractional derivatives
Sign Up to like & getrecommendations! Published in 2018 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-017-0536-8
Abstract: We propose a new fractional derivative, the Hilfer–Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer–Hadamard, Riemann–Liouville, Hadamard, Caputo, Caputo–Hadamard, Liouville, Weyl, generalized and Caputo-type. As… read more here.
Keywords: derivatives hilfer; caputo; hilfer katugampola; katugampola fractional ... See more keywords
On stability of nonlinear nonautonomous discrete fractional Caputo systems
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.124021
Abstract: Abstract Conditions to establish Mittag-Leffler stability of solutions for nonlinear nonautonomous discrete Caputo-like fractional systems just from the linear associated system is shown. Mittag-Leffler stability for linear systems is tackled pointing out properties the matrix… read more here.
Keywords: caputo; nonlinear nonautonomous; leffler stability; mittag leffler ... See more keywords
Extension of rate of change concept: From local to nonlocal operators with applications
Sign Up to like & getrecommendations! Published in 2020 at "Results in physics"
DOI: 10.1016/j.rinp.2020.103515
Abstract: Abstract The concept of rate of change gave birth to numerous important theories and applications in mathematics, applied mathematics and other related academic disciplines. For example, differential calculus which is linked to integral calculus via… read more here.
Keywords: caputo; change; calculus; function ... See more keywords
Soret Effect on MHD Casson Fluid over an Accelerated Plate with the Help of Constant Proportional Caputo Fractional Derivative
Sign Up to like & getrecommendations! Published in 2024 at "ACS Omega"
DOI: 10.1021/acsomega.3c07311
Abstract: Non-Newtonian fluid flow is significant in engineering and biomedical applications such as thermal exchangers, electrical cooling mechanisms, nuclear reactor cooling, drug delivery, blood flow analysis, and tissue engineering. The Caputo operator has emerged as a… read more here.
Keywords: caputo; plate; fluid; constant proportional ... See more keywords
Existence theory and numerical solutions to smoking model under Caputo-Fabrizio fractional derivative.
Sign Up to like & getrecommendations! Published in 2019 at "Chaos"
DOI: 10.1063/1.5079644
Abstract: In this paper, taking fractional derivative due to Caputo and Fabrizo, we have investigated a biological model of smoking type. By using Sumudu transform and Picard successive iterative technique, we develop the iterative solutions for… read more here.
Keywords: caputo; numerical solutions; fractional derivative; model ... See more keywords
Generalized fractional viscothermoelastic nanobeam under the classical Caputo and the new Caputo–Fabrizio definitions of fractional derivatives
Sign Up to like & getrecommendations! Published in 2021 at "Waves in Random and Complex Media"
DOI: 10.1080/17455030.2021.1883767
Abstract: In this paper, we introduce a new unified formula that governs two different definitions of fractional derivative; the classical Caputo definition and Caputo–Fabrizio's new definition. Hence, an an... read more here.
Keywords: caputo; caputo fabrizio; generalized fractional; classical caputo ... See more keywords
The method of Φ-Laplace Adomian decomposition for Φ-Caputo fractional Bloch equations
Sign Up to like & getrecommendations! Published in 2025 at "Physica Scripta"
DOI: 10.1088/1402-4896/adfd2f
Abstract: This article studies the Bloch equations (BEs), which form a system of macroscopic equations used for the simulation of nuclear magnetization as a function of time, when the relaxation times T1 and T2 are given.… read more here.
Keywords: laplace; bloch equations; caputo; adomian decomposition ... See more keywords
A Novel Efficient Approach for Solving Nonlinear Caputo Fractional Differential Equations
Sign Up to like & getrecommendations! Published in 2024 at "Advances in Mathematical Physics"
DOI: 10.1155/2024/1971059
Abstract: Several scientific areas utilize fractional nonlinear partial differential equations (PDEs) to model various phenomena, yet most of these equations lack exact solutions (Ex‐Ss). Consequently, techniques for obtaining approximate solutions (App‐S), which sometimes yield Ex‐Ss, are… read more here.
Keywords: differential equations; solving nonlinear; caputo; series ... See more keywords
Existence of solutions to a fractional differential equation involving the Caputo q-derivative with boundary conditions in Banach spaces
Sign Up to like & getrecommendations! Published in 2025 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-025-03302-w
Abstract: Generalized boundary value problems (BVP) typically cover a wide range of equations. In this study, we focus on a generalization of Caputo-type fractional discrete differential equations that involve two or more fractional q-integrals. We analyze… read more here.
Keywords: equation involving; fractional differential; differential equation; solutions fractional ... See more keywords