Results 21 to 30 of about 1,816,969 (371)

New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model [PDF]

, 2016
In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.
A. Atangana, D. Baleanu
semanticscholar   +1 more source

Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives

, 2021
A newly proposed p -Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives.
M. Matar, M. Abbas, J. Alzabut, Mohammed K. A. Kaabar, S. Etemad, S. Rezapour   +5 more
semanticscholar   +1 more source

On Λ-Fractional Analysis and Mechanics

Axioms, 2022
Λ-Fractional analysis was introduced to fill up the mathematical gap exhibited in fractional calculus, where the various fractional derivatives fail to fulfill the prerequisites demanded by differential topology.
Konstantinos A. Lazopoulos
doaj   +1 more source

On the General Solutions of Some Non-Homogeneous Div-Curl Systems with Riemann–Liouville and Caputo Fractional Derivatives

Fractal and Fractional, 2021
In this work, we investigate analytically the solutions of a nonlinear div-curl system with fractional derivatives of the Riemann–Liouville or Caputo types.
B. Delgado, J. Macías-Díaz
semanticscholar   +1 more source

Fractional derivatives and the fundamental theorem of fractional calculus [PDF]

, 2020
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 under some reasonable conditions, there exists precisely one unique family of
Yuri Luchko
semanticscholar   +1 more source

Solvability of Langevin equations with two Hadamard fractional derivatives via Mittag–Leffler functions [PDF]

Applicable Analysis, 2020
In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method of this discussion is to study the solutions of the equivalent Volterra integral equation in terms of Mittag–Leffler functions.
M. Abbas, M. Alessandra Ragusa
semanticscholar   +1 more source

Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics, 2021
In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator.
Fátima Cruz, Ricardo Almeida, Natália Martins   +2 more
doaj   +1 more source

Generalized fractional derivatives and Laplace transform

Discrete and Continuous Dynamical Systems. Series A, 2020
In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions.
F. Jarad, T. Abdeljawad
semanticscholar   +1 more source

On the fractional deformation of a linearly elastic bar

Journal of the Mechanical Behavior of Materials, 2020
Fractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local ...
Lazopoulos Konstantinos A., Lazopoulos Anastasios K.   +1 more
doaj   +1 more source

Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations

Journal of Advanced Research, 2023
Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement ...
Mohammad Hossein Heydari, Mohsen Razzaghi, Dumitru Baleanu   +2 more
doaj   +1 more source