scholarly journals Regarding on the exact solutions for the nonlinear fractional differential equations

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 478-482 ◽  
Author(s):  
Melike Kaplan ◽  
Murat Koparan ◽  
Ahmet Bekir
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Simple Equation ◽  
Wave Transformation ◽  
Nonlinear Ordinary Differential Equations ◽  
Fractional Order Differential Equations ◽  
Fractional Differential

AbstractIn this work, we have considered the modified simple equation (MSE) method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW) and the modified equal width (mEW) equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

scholarly journals An effective technique for the conformable space-time fractional EW and modified EW equations

2019 ◽  
Vol 8 (1) ◽  
pp. 157-163 ◽  
Author(s):  
K. Hosseini ◽  
A. Bekir ◽  
F. Rabiei
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Traveling Wave ◽  
Expansion Method ◽  
Space Time ◽  
Wave Transformation ◽  
Nonlinear Ordinary Differential Equations ◽  
Effective Technique ◽  
Fractional Models

AbstractThe current work deals with the fractional forms of EW and modified EW equations in the conformable sense and their exact solutions. In this respect, by utilizing a traveling wave transformation, the governing space-time fractional models are converted to the nonlinear ordinary differential equations (NLODEs); and then, the resulting NLODEs are solved through an effective method called the exp(−ϕ(ϵ))-expansion method. As a consequence, a number of exact solutions to the fractional forms of EW and modified EW equations are generated.

scholarly journals General solution of Bernoulli and Riccati fractional differential equations based on conformable fractional derivative

2017 ◽  
Vol 6 (2) ◽  
pp. 49 ◽  
Author(s):  
Zainab Ayati ◽  
Jafar Biaar ◽  
Mousa Ilei
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Riccati Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Conformable Fractional Derivative ◽  
Numerical Examples ◽  
Fractional Differential

This paper is aimed to develop two well-known nonlinear ordinary differential equations, Bernoulli and Riccati equations to fractional form. General solution to fractional differential equations are detected, based on conformable fractional derivative. For each equation, numerical examples are presented to illustrate the proposed approach.  

scholarly journals Solutions for Impulsive Fractional Differential Equations via Variational Methods

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Peiluan Li ◽  
Hui Wang ◽  
Zheqing Li
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Critical Points ◽  
Existence Results ◽  
Fractional Order Differential Equations ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We investigate the boundary value problems of impulsive fractional order differential equations. First, we obtain the existence of at least one solution by the minimization result of Mawhin and Willem. Then by the variational methods and a very recent critical points theorem of Bonanno and Marano, the existence results of at least triple solutions are established. At last, two examples are offered to demonstrate the application of our main results.

scholarly journals Non-instantaneous impulses in Caputo fractional differential equations

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Ravi Agarwal ◽  
Snezhana Hristova ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Real World ◽  
Existence Results ◽  
Advantages And Disadvantages ◽  
Fractional Order Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

AbstractRecent modeling of real world phenomena give rise to Caputo type fractional order differential equations with non-instantaneous impulses. The main goal of the survey is to highlight some basic points in introducing non-instantaneous impulses in Caputo fractional differential equations. In the literature there are two approaches in interpretation of the solutions. Both approaches are compared and their advantages and disadvantages are illustrated with examples. Also some existence results are derived.

scholarly journals Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmet Bekir ◽  
Özkan Güner ◽  
Adem C. Cevikel
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Function Method ◽  
Fractional Derivatives ◽  
Fractional Complex Transform ◽  
Fractional Equations ◽  
New Exact Solutions ◽  
Fractional Differential

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. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

scholarly journals APPLICATIONS OF BI-FRAMELET SYSTEMS FOR SOLVING FRACTIONAL ORDER DIFFERENTIAL EQUATIONS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040051 ◽  
Author(s):  
MUTAZ MOHAMMAD ◽  
CARLO CATTANI
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sparse Matrices ◽  
Computational Method ◽  
Extension Principle ◽  
Vanishing Moments ◽  
Fractional Order Differential Equations ◽  
Fractional Differential

Framelets and their attractive features in many disciplines have attracted a great interest in the recent years. This paper intends to show the advantages of using bi-framelet systems in the context of numerical fractional differential equations (FDEs). We present a computational method based on the quasi-affine bi-framelets with high vanishing moments constructed using the generalized (mixed) oblique extension principle. We use this system for solving some types of FDEs by solving a series of important examples of FDEs related to many mathematical applications. The quasi-affine bi-framelet-based methods for numerical FDEs show the advantages of using sparse matrices and its accuracy in numerical analysis.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals Exact solutions of conformable fractional differential equations

2021 ◽  
Vol 22 ◽  
pp. 103916
Author(s):  
Haleh Tajadodi ◽  
Zareen A. Khan ◽  
Ateeq ur Rehman Irshad ◽  
J.F. Gómez-Aguilar ◽  
Aziz Khan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Fractional Differential
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