Journal ArticleDOI
The first integral method for Wu---Zhang system with conformable time-fractional derivative
Mostafa Eslami,Hadi Rezazadeh +1 more
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In this article, the first integral method was used to construct exact solutions of the Wu-Zhang system, which is based on the ring theory of commutative algebra, and the results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.Abstract:
In this paper, the first integral method is used to construct exact solutions of the time-fractional Wu---Zhang system. Fractional derivatives are described by conformable fractional derivative. This method is based on the ring theory of commutative algebra. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.read more
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General conformable fractional derivative and its physical interpretation
Dazhi Zhao,Maokang Luo +1 more
TL;DR: In this paper, a general conformable fractional derivative (GCFD) is proposed to describe the physical world, which is generalized from the concept of CFD proposed by Khalil.
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New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity
TL;DR: In this article, a new solitons solution of the complex Ginzburg-Landau equation with Kerr law nonlinearity was found using the new extended direct algebraic method.
Journal ArticleDOI
New exact solutions of Burgers’ type equations with conformable derivative
TL;DR: In this paper, the exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative of the Burgers-Korteweg-de Vries equation.
Journal ArticleDOI
Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations
TL;DR: By using the Kudryashov method, new conformable fractional derivative is applied for converting fractional coupled nonlinear Schrodinger equations into the ordinary differential equations and new traveling wave solutions are extracted.
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Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation
TL;DR: In this paper, a conformable (2+1)-dimensional Ablowitz-KaupNewell-Segur equation is studied and the existence of complex combined dark-bright soliton solutions is shown.
References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Journal ArticleDOI
A new definition of fractional derivative
TL;DR: A new definition of fractional derivative and fractional integral is given and it is shown that it is the most natural definition, and the most fruitful one.