Results 11 to 20 of about 760,461 (313)

Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial

Mathematics, 2018
Solving differential equations of fractional (i.e., non-integer) order in an accurate, reliable and efficient way is much more difficult than in the standard integer-order case; moreover, the majority of the computational tools do not provide built-in ...
R. Garrappa
semanticscholar   +3 more sources

Linear differential equations with variable coefficients and Mittag-Leffler kernels

Alexandria Engineering Journal, 2022
Fractional differential equations with constant coefficients can be readily handled by a number of methods, but those with variable coefficients are much more challenging.
Arran Fernandez, Joel E. Restrepo, Durvudkhan Suragan   +2 more
doaj   +1 more source

On the Stability and Numerical Scheme of Fractional Differential Equations with Application to Biology

De Computis, 2022
The fractional differential equations involving different types of fractional derivatives are currently used in many fields of science and engineering. Therefore, the first purpose of this study is to investigate the qualitative properties including the ...
K. Hattaf
semanticscholar   +1 more source

On Laplace transforms with respect to functions and their applications to fractional differential equations

Mathematical methods in the applied sciences, 2021
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called Ψ‐fractional calculus.
Hafiz Muhammad Fahad, M. Rehman, A. Fernandez   +2 more
semanticscholar   +1 more source

On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

Symmetry, 2021
This paper deals with a new class of hybrid fractional differential equations with fractional proportional derivatives of a function with respect to a certain continuously differentiable and increasing function ϑ. By means of a hybrid fixed point theorem
M. Abbas, M. Ragusa
semanticscholar   +1 more source

Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications

Mathematical Methods in the Applied Sciences, 2018
R. Almeida, A. Malinowska, M. T. Monteiro   +2 more
semanticscholar   +3 more sources

The amazing fractional Maclaurin series for solving different types of fractional mathematical problems that arise in physics and engineering

Partial Differential Equations in Applied Mathematics, 2023
Many applications and natural phenomena in the fields of physics and engineering are described by ordinary and partial differential equations. Therefore, obtaining solutions to these equations helps to analyze and understand the dynamics of these systems,
Marwan Alquran
doaj   +1 more source

The modified generalized Kudryashov method for nonlinear space–time fractional partial differential equations of Schrödinger type

Results in Physics, 2023
This paper presents a modified version of the generalized Kudryashov method aimed at obtaining exact solutions for fractional partial differential equations of Schrödinger type.
Fushun Liu, Yuqiang Feng
doaj   +1 more source

Linearized Asymptotic Stability for Fractional Differential Equations [PDF]

, 2016
We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the ...
Cong, N. D., Doan, T. S., Siegmund, S., Tuan, H. T.   +3 more
core   +3 more sources

Exact solutions of conformable fractional differential equations

, 2021
This article is about to formulate exact solutions of the time fractional Dodd-Bullough-Mikhailov (DBM) equation, Sinh-Gordon equation and Liouville equation by utilizing simplest equation method (SEM) in conformable fractional derivative (CFD) sense ...
H. Tajadodi, Z. Khan, A. Irshad, J. F. Gómez‐Aguilar, Aziz Khan, H. Khan   +5 more
semanticscholar   +1 more source