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 A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2166
Author(s):  
Tofigh Allahviranloo ◽  
Zahra Noeiaghdam ◽  
Samad Noeiaghdam ◽  
Juan J. Nieto
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Taylor Expansion ◽  
Direct Method ◽  
Numerical Examples ◽  
Euler’S Method ◽  
Truncation Errors ◽  
Fractional Differential ◽  
Fuzzy Fractional Differential Equations

In this field of research, in order to solve fuzzy fractional differential equations, they are normally transformed to their corresponding crisp problems. This transformation is called the embedding method. The aim of this paper is to present a new direct method to solve the fuzzy fractional differential equations using fuzzy calculations and without this transformation. In this work, the fuzzy generalized Taylor expansion by using the sense of fuzzy Caputo fractional derivative for fuzzy-valued functions is presented. For solving fuzzy fractional differential equations, the fuzzy generalized Euler’s method is introduced and applied. In order to show the accuracy and efficiency of the presented method, the local and global truncation errors are determined. Moreover, the consistency, convergence, and stability of the generalized Euler’s method are proved in detail. Eventually, the numerical examples, especially in the switching point case, show the flexibility and the capability of the presented method.

scholarly journals Kamenev Type Oscillatory Criteria for Linear Conformable Fractional Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Shao ◽  
Zhaowen Zheng
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Average Method ◽  
Oscillation Theory ◽  
Conformable Fractional Derivative ◽  
Oscillation Criteria ◽  
Fractional Differential ◽  
Type Oscillation ◽  
Integral Average

Using integral average method and properties of conformable fractional derivative, new Kamenev type oscillation criteria are given firstly for conformable fractional differential equations, which improve known results in oscillation theory. Examples are also given to illustrate the effectiveness of the main results.

scholarly journals General solution of second order fractional differential equations

2018 ◽  
Vol 7 (2) ◽  
pp. 56 ◽  
Author(s):  
Mousa Ilie ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Second Order ◽  
Conformable Fractional Derivative ◽  
High Importance ◽  
Particular Solution ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations ◽  
General Method

Fractional differential equations are often seeming perplexing to solve. Therefore, finding comprehensive methods for solving them sounds of high importance. In this paper, a general method for solving second order fractional differential equations has been presented based on conformable fractional derivative. This method realizes on determining a general solution of homogeneous and a particular solution of a second order linear fractional differential equations. Furthermore, a general solution has been developed for fractional Euler’s equation. For more explanation of each part, some examples have been solved. 

scholarly journals Hille and Nehari Type Oscillation Criteria for Conformable Fractional Differential Equations

2021 ◽  
pp. 578-587
Author(s):  
T. Gayathri ◽  
M. Sathish Kumar ◽  
V. Sadhasivam
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Conformable Fractional Derivative ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Fractional Differential ◽  
Type Oscillation ◽  
Comparison Technique

In this paper, we develop the Hille and Nehari Type criteria for the oscillation of all solutions to the Fractional Differential Equations involving Conformable fractional derivative. Some new oscillatory criteria are obtained by using the Riccati transformations and comparison technique. We show the validity and effectiveness of our results by providing various examples.

scholarly journals A New Attractive Method in Solving Families of Fractional Differential Equations by a New Transform

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3039
Author(s):  
Ahmad Qazza ◽  
Aliaa Burqan ◽  
Rania Saadeh
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Integral Transform ◽  
Series Solutions ◽  
Numerical Examples ◽  
Fractional Differential ◽  
Expansion Coefficients

In this paper, we use the ARA transform to solve families of fractional differential equations. New formulas about the ARA transform are presented and implemented in solving some applications. New results related to the ARA integral transform of the Riemann-Liouville fractional integral and the Caputo fractional derivative are obtained and the last one is implemented to create series solutions for the target equations. The procedure proposed in this article is mainly based on some theorems of particular solutions and the expansion coefficients of binomial series. In order to achieve the accuracy and simplicity of the new method, some numerical examples are considered and solved. We obtain the solutions of some families of fractional differential equations in a series form and we show how these solutions lead to some important results that include generalizations of some classical methods.

scholarly journals Improvement on Conformable Fractional Derivative and Its Applications in Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Feng Gao ◽  
Chunmei Chi
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Physical Meaning ◽  
Fractional Integral ◽  
Conformable Fractional Derivative ◽  
Conformable Derivative ◽  
Fractional Differential ◽  
Definition Of

In this paper, we made improvement on the conformable fractional derivative. Compared to the original one, the improved conformable fractional derivative can be a better replacement of the classical Riemann-Liouville and Caputo fractional derivative in terms of physical meaning. We also gave the definition of the corresponding fractional integral and illustrated the applications of the improved conformable derivative to fractional differential equations by some examples.

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 Analytical solutions for conformable fractional Bratu-type equations

2018 ◽  
Vol 7 (1) ◽  
pp. 15 ◽  
Author(s):  
Mousa Ilie ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Analytical Method ◽  
Conformable Fractional Derivative ◽  
Fractional Differential

Solving fractional differential equations have a prominent function in different science such as physics and engineering. Therefore, are different definitions of the fractional derivative presented in recent years. The aim of the current paper is to solve the fractional differential equation by a semi-analytical method based on conformable fractional derivative. Fractional Bratu-type equations have been solved by the method and to show its capabilities. The obtained results have been compared with the exact solution.

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