Results 11 to 20 of about 184,534 (322)

Large Fractional Linear Type Differential Equations

International Journal of Analysis and Applications, 2023
This paper aims to handle some types of fractional differential equations with a fractional-order values β>1. In particular, we propose a novel analytical solution called an atomic solution for certain fractional linear type differential equations as ...
Ma'mon Abu Hammad, Iqbal Jebril, Roshdi Khalil   +2 more
doaj   +1 more source

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

Effects of the ARA transform method for time fractional problems [PDF]

Mathematica Moravica, 2022
The aim of this study is to establish the solutions of time fractional mathematical problems with the aid of new integral transforms called the ARA transform. The fractional derivative is taken in the sense of Liouville-Caputo derivative.
Çetınkaya Süleyman, Demir Ali
doaj   +1 more source

Coupled systems of fractional equations related to sound propagation: analysis and discussion [PDF]

, 2012
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in the ...
Diethelm K., Federico Polito, Fellah Z. E. A., Haubold H. J., Kilbas A. A., Podlubny I., Roberto Garra   +6 more
core   +1 more source

Mixed Order Fractional Differential Equations [PDF]

Mathematics, 2017
This paper studies fractional differential equations (FDEs) with mixed fractional derivatives. Existence, uniqueness, stability, and asymptotic results are derived.
Michal Fečkan, JinRong Wang
openaire   +3 more sources

Generalized iterative method for the solution of linear and nonlinear fractional differential equations with composite fractional derivative operator

AIMS Mathematics, 2020
In present paper, we introduced generalized iterative method to solve linear and nonlinear fractional differential equations with composite fractional derivative operator.
Krunal B. Kachhia, Jyotindra C. Prajapati   +1 more
doaj   +1 more source

Wavelets operational methods for fractional differential equations and systems of fractional differential equations [PDF]

, 2017
In this thesis, new and effective operational methods based on polynomials and wavelets for the solutions of FDEs and systems of FDEs are developed.
A. H. Al-Bagawi, A. H. Al-Bagawi, Abdo Alkhadhera, Sadeq Abdullah, Abdul Kadir, Aeslina, Al-Gheethi, Adel, M. Magam, Sami, Masood, Najat, Suratman, Suhaimi, Y. A. Alanazid, Tahani, Zakaria, Mohamad Pauzi   +8 more
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Existence of the Solution for System of Coupled Hybrid Differential Equations with Fractional Order and Nonlocal Conditions

International Journal of Differential Equations, 2016
This paper is motivated by some papers treating the fractional hybrid differential equations with nonlocal conditions and the system of coupled hybrid fractional differential equations; an existence theorem for fractional hybrid differential equations ...
Khalid Hilal, Ahmed Kajouni
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
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Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

Abstract and Applied Analysis, 2013
The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations.
Ahmet Bekir, Özkan Güner, Adem C. Cevikel   +2 more
doaj   +1 more source