scholarly journals Adequate Soliton Solutions to the Space-Time Fractional Telegraph Equation and Modified Third-Order KdV Equation through A Reliable Technique

2021 ◽  
Author(s):  
Ummay Sadia ◽  
Mohammad Asif Arefin ◽  
Mustafa Inc ◽  
M. Hafiz Uddin
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Traveling Wave ◽  
Telegraph Equation ◽  
Space Time ◽  
Nonlinear Evolution Equations ◽  
Communication Line ◽  
Third Order ◽  
Wave Solutions ◽  
Fractional Telegraph Equation

Abstract The space-time fractional telegraph equation and the space-time fractional modified third-order Kdv equations are significant molding equations in theoretic physics, mathematical physics, plasma physics also other fields of nonlinear sciences. The space time-fractional telegraph equation, which appears in the investigation of an electrical communication line and includes voltage in addition to current which is dependent on distance and time, is also applied to communication lines of wholly frequencies, together with direct current, as well as high-frequency conductors, audio frequency (such as telephone lines), and low frequency (for example cable television) used in the extension of pressure waves into the lessons of pulsatory blood movement among arteries also the one-dimensional haphazard movement of bugs towards an obstacle. The presence of chain rule and the derivative of composite functions allows the nonlinear fractional differential equations (NLFDEs) to translate into the ordinary differential equation employing wave alteration. To explore such categories of resolutions, the extended tanh-method is accomplished via Conformable fractional derivatives. A power sequence in tanh was originally used as an ansatz to provide analytical solutions of the traveling wave type of certain nonlinear evolution equations. To convert this problem to a standard differential equation, a partial complex transformation that has been summarized succinctly is utilized correctly thus, with all of the free parameters, numerous exact logical arrangements are required. The results are found as hyperbolic and rational functions involving parameters, when specific values are supplied to the parameters solitary wave solutions are formed from traveling wave solutions. The outcomes achieved in this study are king type, single soliton, double soliton, multiple solitons, bell shape, and other sorts of forms and we demonstrated that these solutions were validated through the Maple software. The proposed approach for solving nonlinear fractional partial differential equations has been developed to be operative, unpretentious, quick, and reliable to usage.

scholarly journals Five semi analytical and numerical simulations for the fractional nonlinear space-time telegraph equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mostafa M. A. Khater ◽  
Choonkil Park ◽  
Jung Rye Lee ◽  
Mohamed S. Mohamed ◽  
Raghda A. M. Attia
Keyword(s):  
Numerical Simulations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Approximate Solutions ◽  
Telegraph Equation ◽  
Space Time ◽  
Numerical Techniques ◽  
B Spline ◽  
Wave Solutions ◽  
Adomian Decomposition

AbstractThe accuracy of analytical obtained solutions of the fractional nonlinear space–time telegraph equation that has been constructed in (Hamed and Khater in J. Math., 2020) is checked through five recent semi-analytical and numerical techniques. Adomian decomposition (AD), El Kalla (EK), cubic B-spline (CBS), extended cubic B-spline (ECBS), and exponential cubic B-spline (ExCBS) schemes are used to explain the matching between analytical and approximate solutions, which shows the accuracy of constructed traveling wave solutions. In 1880, Oliver Heaviside derived the considered model to describe the cutting-edge or voltage of an electrified transmission. The matching between solutions has been explained by plotting them in some different sketches.

New types of soliton solutions for space-time fractional cubic nonlinear Schrodinger equation

2021 ◽  
Vol 39 (2) ◽  
pp. 121-131
Author(s):  
Ahmad Neirameh ◽  
Mostafa Eslami ◽  
Mostafa Mehdipoor
Keyword(s):  
Schrödinger Equation ◽  
Differential Equations ◽  
Nonlinear Schrödinger Equation ◽  
Traveling Wave ◽  
Schrodinger Equation ◽  
Space Time ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Schrödinger ◽  
Cubic Nonlinear Schrödinger Equation

New definitions for traveling wave transformation and using of new conformable fractional derivative for converting fractional nonlinear evolution equations into the ordinary differential equations are presented in this study. For this aim we consider the time and space fractional derivatives cubic nonlinear Schrodinger equation. Then by using of the efficient and powerful method the exact traveling wave solutions of this equation are obtained. The new definition introduces a promising tool for solving many space-time fractional partial differential equations.

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

Open Physics ◽  
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.

scholarly journals Generalized Weierstrass Integrability of a Class of Second-order Nonlinear Differential Equations

2021 ◽  
pp. 119-133
Author(s):  
Xin Zhao ◽  
Yanxia Hu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Second Order ◽  
Wave Solutions ◽  
The Relationship ◽  
Integrating Factors

The generalized Weierstrass integrability of a class of second-order nonlinear differential equations is considered. The conditions of existence and the corresponding expressions of generalized Weierstrass inverse integrating factors of the second-order nonlinear differential equation are presented. The relationship between the generalized Weierstrass inverse integrating factors and the Weierstrass inverse integrating factors is given. Finally, as an application of the main results, a Kudryashov-Sinelshchikov equation for obtaining traveling wave solutions is considered.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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