In the present work, we systematically derive the invariant subspaces for nonlinear time-fractional differential equations in the Hilfer sense and illustrate its applicability through physically significant equations such as the time-fractional heat equation, time fractional Burgers equation, time fractional KdV equation, and time fractional Hunter Saxton equation in the Hilfer sense. We also propose the invariant subspace method to time-space fractional partial differential equations involving the one-dimensional fractional Laplacian. We consider the representation of fractional Laplacian as self-induced onedimensional Riesz potential. Our investigation reveals that linear fractional partial differential equations with the one-dimensional Riesz potential admit the exponential type invariant subspaces. Furthermore, we explore various forms of quadratic nonlinear fractional differential equations that admit the exponential invariant subspaces. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
This article investigates the mathematical models of amperometric biosensors. The given models is constructed which depends on diffusion equations of the non-linear element pertaining with an enzyme process. The approximate analytical solutions for both time-independent and time-dependent conditions of concentrations are provided in non-dimensional and dimensional for all values of the parameters. The semi-analytical expressions for the substrate, product concentrations and current are attained by utilising the new homotopy perturbation method (NHPM). The new homotopy perturbation technique is employing to solve the biosensors models like non-linear reaction-diffusion model in amperometric biosensors, potentiometric biosensors and michaelis-menten kinetics. On comparing the numerical simulation with our findings, a good fit is reached. The impacts of several parameters, including the Thiele modulus, saturation parameter, maximal enzymatic rate, the ratio of diffusion coefficients, Michaelis constant, substrate concentration in the bulk solution and thickness of the enzyme membrane are graphically represented for concentration and current. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
A new seven-term 4D hyperjerk system is derived from a homogeneous fourth-order differential equation. This system incorporates cross-product and cubic nonlinearities, resulting in a chaotic attractor. Its dynamic behavior is analyzed through numerical simulations and analytical studies, employing phase portraits, Lyapunov exponents, and the Kaplan-Yorke dimension. Additionally, an electronic circuit representation of the proposed system is designed using Multisim 14.3 software, with observations performed via an oscilloscope and a Tektronix oscilloscope. Numerical simulations confirm the accuracy of the electronic circuit, demonstrating strong consistency with results obtained using MATLAB 23 software. Lastly, the NIST statistical test (SP800-22) is applied to the generated chaotic sequences. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
This work conducts a detailed exploration of exact wave solutions for higher-dimensional Boussinseq-Kadomtsev-Petviashvili (KP) model. By utilizing the improved modified extended tanh-function (IMETF) technique, we derive analytical solutions to the governing equation which describes the wave propagation in fluid dynamics. These solutions include dark, bright, and combined bright-dark solitons, as well as rational, exponential, singular periodic, Jacobi elliptic, and Weierstrass elliptic doubly periodic solutions. Graphical representations are provided to highlight the physical characteristics of the results. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
