Distinct solutions of nonlinear space–time fractional evolution equations appearing in mathematical physics via a new technique

PurposeFractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering.Design/methodology/approachThe rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i.FindingsAchieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.Originality/valueThe rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.

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Fractional quasi AKNS‐technique for nonlinear space–time fractional evolution equations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5633 ◽

2019 ◽

Vol 42 (18) ◽

pp. 5953-5968 ◽

Cited By ~ 3

Author(s):

Emad A.‐B. Abdel‐Salam ◽

Mohamed F. Mourad

Keyword(s):

Evolution Equations ◽

Space Time ◽

Fractional Evolution Equations

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Generalized Robertson-Walker Space-Time Admitting Evolving Null Horizons Related to a Black Hole Event Horizon

International Scholarly Research Notices ◽

10.1155/2016/9312525 ◽

2016 ◽

Vol 2016 ◽

pp. 1-6

Author(s):

K. L. Duggal

Keyword(s):

Black Hole ◽

Event Horizon ◽

Space Time ◽

Time Dependent ◽

New Technique ◽

Open Problems ◽

Totally Umbilical ◽

Kinematic Condition ◽

A New Technique

A new technique is used to study a family of time-dependent null horizons, called “Evolving Null Horizons” (ENHs), of generalized Robertson-Walker (GRW) space-time (M¯,g¯) such that the metric g¯ satisfies a kinematic condition. This work is different from our early papers on the same issue where we used (1+n)-splitting space-time but only some special subcases of GRW space-time have this formalism. Also, in contrast to previous work, we have proved that each member of ENHs is totally umbilical in (M¯,g¯). Finally, we show that there exists an ENH which is always a null horizon evolving into a black hole event horizon and suggest some open problems.

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Stochastic classical solutions for space–time fractional evolution equations on a bounded domain

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2018.09.030 ◽

2019 ◽

Vol 469 (2) ◽

pp. 594-622 ◽

Cited By ~ 3

Author(s):

Lorenzo Toniazzi

Keyword(s):

Bounded Domain ◽

Evolution Equations ◽

Space Time ◽

Classical Solutions ◽

Fractional Evolution Equations

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Algebraic computational methods for solving three nonlinear vital models fractional in mathematical physics

Open Physics ◽

10.1515/phys-2021-0020 ◽

2021 ◽

Vol 19 (1) ◽

pp. 152-169

Author(s):

Khaled A. Gepreel ◽

Amr M. S. Mahdy

Keyword(s):

Differential Equations ◽

Evolution Equations ◽

Soliton Solutions ◽

Algebraic Method ◽

Mathematical Physics ◽

Space Time ◽

Nonlinear Evolution Equations ◽

Hyperbolic Function ◽

Wave Solutions ◽

Elliptic Solutions

Abstract This research paper uses a direct algebraic computational scheme to construct the Jacobi elliptic solutions based on the conformal fractional derivatives for nonlinear partial fractional differential equations (NPFDEs). Three vital models in mathematical physics [the space-time fractional coupled Hirota Satsuma KdV equations, the space-time fractional symmetric regularized long wave (SRLW equation), and the space-time fractional coupled Sakharov–Kuznetsov (S–K) equations] are investigated through the direct algebraic method for more explanation of their novel characterizes. This approach is an easy and powerful way to find elliptical Jacobi solutions to NPFDEs. The hyperbolic function solutions and trigonometric functions where the modulus and, respectively, are degenerated by Jacobi elliptic solutions. In this style, we get many different kinds of traveling wave solutions such as rational wave traveling solutions, periodic, soliton solutions, and Jacobi elliptic solutions to nonlinear evolution equations in mathematical physics. With the suggested method, we were fit to find much explicit wave solutions of nonlinear integral differential equations next converting them into a differential equation. We do the 3D and 2D figures to define the kinds of outcome solutions. This style is moving, reliable, powerful, and easy for solving more difficult nonlinear physics mathematically.

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