Conformable Fractional Derivatives and It Is Applications for Solving Fractional Differential Equations

Published on Apr 1, 2017in IOSR Journal of Mathematics
· DOI :10.9790/5728-1302028187
Ahmed Murshed Kareem1
Estimated H-index: 1
Source
Abstract
📖 Papers frequently viewed together
1 Citations
2020
4 Citations
References2
Newest
#1Roshdi Khalil (UJ: University of Jordan)H-Index: 13
#2M. Al Horani (UJ: University of Jordan)H-Index: 4
Last. Mohammad Sababheh (UOS: University of Sharjah)H-Index: 9
view all 4 authors...
We give a new definition of fractional derivative and fractional integral. The form of the definition shows that it is the most natural definition, and the most fruitful one. The definition for [email protected][email protected]<1 coincides with the classical definitions on polynomials (up to a constant). Further, if @a=1, the definition coincides with the classical definition of first derivative. We give some applications to fractional differential equations.
1,120 CitationsSource
#1Igor PodlubnyH-Index: 1
Preface. Acknowledgments. Special Functions Of Preface. Acknowledgements. Special Functions of the Fractional Calculus. Gamma Function. Mittag-Leffler Function. Wright Function. Fractional Derivatives and Integrals. The Name of the Game. Grunwald-Letnikov Fractional Derivatives. Riemann-Liouville Fractional Derivatives. Some Other Approaches. Sequential Fractional Derivatives. Left and Right Fractional Derivatives. Properties of Fractional Derivatives. Laplace Transforms of Fractional Derivative...
2,626 Citations
Cited By7
Newest
Abstract In this paper, we proceed on to develop the classical Natural transform to fractional order in the sense of conformable derivative and set the basic concepts in this new interesting fractional transform version. The conformable fractional Natural transform of certain functions, properties and relationships are derived and discussed. Furthermore, we present the general analytical solution of a generalized conformable Bernoulli’s fractional differential equation based on the new version a...
3 CitationsSource
#2Wenjun LiuH-Index: 63
Last. Jian DingH-Index: 1
view all 3 authors...
In this paper, we consider the bifurcation method of dynamical systems for solving time fractional nonlinear evolution equations. We adapt and modify the methodology, incorporating new ideas from the conformable fractional derivative, to investigate exact travelling wave solutions and bifurcations of phase transitions for nonlinear evolution equations. In this study, we show the existence of periodic wave solutions, kink and anti-kink wave solutions, a bright and dark solitary wave solution and ...
Source
The current article studied a nonlinear transmission of the nerve impulse model, the Fitzhugh–Nagumo (FN) model, in the conformable fractional form with an efficient analytical approach based on a combination of conformable Sumudu transform and the Adomian decomposition method. Convergence analysis and error analysis were also carried out based on the Banach fixed point theory. We also provided some examples to support our results. The results obtained revealed that the presented approach is ver...
Source
#1Limei Feng (UJN: University of Jinan)H-Index: 1
#2Shurong Sun (UJN: University of Jinan)H-Index: 24
In this paper, we consider the oscillation theory for fractional differential equations. We obtain oscillation criteria for three classes of fractional differential equations of the forms $$\begin{aligned}& T_{\alpha}^{t_{0}} x(t)+\sum_{i=1}^{m}p_{i}(t)x \bigl(\tau_{i}(t)\bigr)=0,\quad t\geqslant t_{0}, \\& T_{\alpha}^{t_{0}} \bigl(r(t) \bigl(T_{\alpha}^{t_{0}} \bigl(x(t)+p(t)x\bigl(\tau(t)\bigr)\bigr)\bigr)^{\beta}\bigr)+q(t)x^{\beta}\bigl(\sigma(t)\bigr)=0, \quad t\geqslant t_{0}, \end{aligned...
6 CitationsSource
Abstract In the present paper, we use efficient and simple algorithms of the fractional power series and Adomain polynomial methods that provide effective tools for solving such linear and nonlinear fractional differential equations in the sense of conformable derivative. The first method succeeded in finding the fractional power series solution for the Laguerre linear fractional differential equation with some important special cases. The second method is applied to predict and construct the fr...
21 CitationsSource
We study a nonlocal thermistor problem for fractional derivatives in the conformable sense. Classical Schauder's fixed point theorem is used to derive the existence of a tube solution.
4 CitationsSource