Sid Ahmed Ould Beinane

This paper addresses multiple inverse source problems linked to the wave equation under nonlocal boundary conditions. A bi-orthogonal functional framework is adopted to represent the solutions through series expansions. The analysis establishes that these problems are ill-posed in the Hadamard sense. Three main reconstruction tasks are considered: identification of an unknown space-dependent source, recovery of the initial data, and estimation of a time-varying source term. For each case, suitable additional conditions are introduced to ensure the uniqueness of the unknown quantities. Existence and uniqueness theorems are proved under specific smoothness requirements. Finally, the theoretical developments are validated through numerical computations.

The study of nanoliquid characteristics and their heat performance have attracted the interest of engineers. These engineered fluids have high thermal conductivity due to which such liquids are reliable for different engineering applications including heating/cooling of buildings, thermal and mechanical engineering, etc. Therefore, the current research design provides a new ternary nanoliquid model for the heat transport process under induced magnetic field effects, mixed convection, heating source and thermal radiations. The modeling has been done by implementing the ternary fluid characteristics and supportive transformations and then for results simulation; bvp4c is coded successfully. It is scrutinized that a higher inductive magnetic field (0.1–0.4) and nanoparticles amount (0.01–0.07) are better to resist the movement while the wedge parameter ([ ] promotes it. By promoting the heating source, Eckert and [ ], the heat transfer process is observed rapidly while the mixed convective number [ ] controls it. Further, the particular used ternary nanoliquid is examined and found to be good for cooling purposes.

In this article, we consider a fractional S E I R model, denoted by the S E I Q H R model, which aims to predict the outbreak of infectious diseases in general. In particular, we study the spread of COVID-19. The fractional order offers a flexible, appropriate, and reliable framework for pandemic growth characterization. Firstly, we analyze some elementary results of the model (boundedness and uniqueness of solutions). In addition, we establish certain conditions to ensure the local stability of the disease-free and endemic equilibrium points. Based on analytical and numerical results, we conclude that coronavirus infection (COVID-19) remains endemic, which requires long-term prevention and intervention strategies.

In this work, we study a time-fractional ion sound and Langmuir waves system (FISLWS) with Atangana–Baleanu derivative (ABD). We use a fractional ABD operator to transform our system into an ODE. We investigate multiwaves, periodic cross-kink, rational, and interaction solutions by the combination of rational, trigonometric, and various bilinear functions. Furthermore, 3D, 2D, and relevant contour plots are presented for the natural evolution of the gained solutions under the selection of proper parameters.

The aim of this work is to build novel analytical wave solutions of the nonlinear space-time fractional (2+1)-dimensional breaking soliton equations, with regards to the modified Riemann–Liouville derivative, by employing mathematical schemes, namely, the improved simple equation and modified F-expansion methods. We used the fractional complex transformation of the concern fractional differential equation to convert it for the solvable integer order differential equation. After the successful implementation of the presented methods, a comprehensive class of novel and broad-ranging exact and solitary travelling wave solutions were discovered, in terms of trigonometric, rational and hyperbolic functions. Hence, the present methods are reliable and efficient for solving nonlinear fractional problems in mathematics physics.