Conformable derivative in a nonlinear dispersive electrical transmission network

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

“…Likewise, the appealing of the beta-derivative enhances and prompts its application at replicating real-world issues regarding abundant scientific investigations that have been stated in numerous research areas. One can cite: nonlinear dispersive electrical transmission network, electrochemical systems, intricate geometries to model electromagnetic waves in dielectric media and cancer treatment [34,[58][59][60]. This well-known applications of the beta-derivatives lead us to consider it like a generalized form of the Caputo and Riemann-Liouville derivatives.…”

“…The whole of these FNEEs, FNPDEs, FNDDEs remains an ongoing task due to the fact that, the power of memory effect is of great interest in the modeling field's. From the mathematical point of view, the classical systems (integer-order derivatives modeling) are not thoughtfully to address this memory effect issue [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Obviously, different researchers demonstrated that, through the fractional-order derivatives (non-integer operators) it is possible to carry out more on memory effect.…”

“…We choose a novel technique to provide new kind of ner-vous impulse of the coupled nerve fibers model studied here. Many methods have been then performed on this NPDE fractional or not, one can cite: the (G ′ (ξ)/G(ξ))expansion mapping method including the generalized Riccati equation [8,34,43], the exp(−ψ(ξ))-expansion function method, the extended (G ′ (ξ)/G 2 (ξ))-expansion method [8,[35][36][37], modified extended Tanh method, modified (G ′ (ξ)/G 2 (ξ))-expansion method [8,52]. Thus, by involving a fractional complex transform (FCT), we refine the model equation, simplify it into a secondorder elliptical NODE.…”