On the Analytical and Numerical Solutions in the Quantum Magnetoplasmas: The Atangana Conformable Derivative (1+3)-ZK Equation with Power-Law Nonlinearity

Abstract

In this research paper, our work is connected with one of the most popular models in quantum magnetoplasma applications. The computational wave and numerical solutions of the Atangana conformable derivative (1+3)-Zakharov-Kuznetsov (ZK) equation with power-law nonlinearity are investigated via the modified Khater method and septic-B-spline scheme. This model is formulated and derived by employing the well-known reductive perturbation method. Applying the modified Khater (mK) method, septic B-spline scheme to the (1+3)-ZK equation with power-law nonlinearity after harnessing suitable wave transformation gives plentiful unprecedented ion-solitary wave solutions. Stability property is checked for our results to show their applicability for applying in the model’s applications. The result solutions are constructed along with their 2D, 3D, and contour graphical configurations for clarity and exactitude.

On the approximate numerical solutions of fractional heat equation with heat source and heat loss

“…The fractional PDEs have taken place in many areas such as viscoelasticity, biology, electronic, signal processing, genetics algorithms, robotic technology, traffic systems, telecommunication, chemistry, physics, economics and finance [1,2,3,4]. Having many applications in these areas has drawn scientists' attention to acquiring the solutions of FPDEs.…”

A Review on Higher Order Spline Techniques for Solving Burgers Equation using B-Spline methods and Variation of B-Spline Techniques

“…This presented work investigates the single and overtaking collision of multi-shock wave excitations having space fractional evolution in a thin viscoelastic tube filled with incompressible inviscid fluid. The computational wave and numerical solutions of the Atangana conformable derivative (1 + 3)-Zakharov-Kuznetsov (ZK) equation with powerlaw nonlinearity are investigated via the modified Khater method and septic-B-spline scheme by M. A. Khater, Y. M Chu [28]. This model is formulated and derived by employing the wellknown reductive perturbation method.…”

Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

“…Furthermore, many research studies have been conducted on the theoretical and practical elements of conformable differential equations shortly after the proposition of this new definition [5,7,12,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Conformable derivative has also been applied in modeling and investigating phenomena in applied sciences and engineering [12] such as the nonlinear Boussinesq equation's travelling wave solutions [36], the coupled nonlinear Schrödinger equations [34] and regularized long wave Burgers equation [35] deterministic and stochastics forms, the approximate long water wave equation's exact solutions [37], the (1 + 3)-Zakharov-Kuznetsov equation with power-law nonlinearity analytical and numerical solutions [38], the (2 + 1)-dimensional Zoomeron equation [39,40] and 3 rd -order modified KdV equation analytical solutions [39], and the exact solutions for Whitham-Broer-Kaup equation's three various models in shallow water [41].…”