Ashraf, RehanaJarad, FahdRashid, Saima02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2024-04-252025-09-182024-04-252025-09-182022Rashid, Saima; Ashraf, Rehana; Jarad, F. (2022). "Strong interaction of Jafari decomposition method with nonlinear fractional-order partial differential equations arising in plasma via the singular and nonsingular kernels", AIMS Mathematics, Vol.7, No.5, pp.7936-7963.2473-6988https://doi.org/10.3934/math.2022444https://hdl.handle.net/123456789/12125This research utilizes the Jafari transform and the Adomian decomposition method to derive a fascinating explicit pattern for the outcomes of the KdV, mKdV, K(2,2) and K(3,3) models that involve the Caputo fractional derivative operator and the Atangana-Baleanu fractional derivative operator in the Caputo sense. The novel exact-approximate solutions are derived from the formulation of trigonometric, hyperbolic, and exponential function forms. Laser and plasma sciences may benefit from these solutions. It is demonstrated that this approach produces a simple and effective mathematical framework for tackling nonlinear problems. To provide additional context for these ideas, simulations are performed, employing a computationally packaged program to assist in comprehending the implications of solutions.eninfo:eu-repo/semantics/openAccessJafari TransformAdomian Decomposition MethodKdv And Mkdv ModelK(2,2) And K(3,3) EquationsArticle10.3934/math.20224442-s2.0-85124913895