Results 21 to 30 of about 760,461 (313)

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

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

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

A generalization of truncated M-fractional derivative and applications to fractional differential equations

Applied Mathematics and Nonlinear Sciences, 2020
In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter ...
Esin İlhana, İ. O. Kıymazb, Esin Ilhan   +2 more
semanticscholar   +1 more source

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

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

Comparison principles for fractional differential equations with the Caputo derivatives

Advances in Difference Equations, 2018
In this paper, we deal with comparison principles for fractional differential equations involving the Caputo derivatives of order p with 0≤n ...
Ziqiang Lu, Yuanguo Zhu
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

On the Nonlinear $\Psi$-Hilfer Hybrid Fractional Differential Equations [PDF]

, 2020
In this paper, we initially derive the equivalent fractional integral equation to $\Psi$-Hilfer hybrid fractional differential equations and through it, we prove the existence of a solution in the weighted space.
Kishor D. Kucche, Ashwini D. Mali
semanticscholar   +1 more source

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Entropy, 2018
In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions.
Xiao-Li Ding, Juan J. Nieto
doaj   +1 more source