A new integral transform method for regularized long-wave (RLW) models having fractional-order is presented in this study. Although analytical approaches are challenging to apply such models, semianalytical or numerical techniques have received much attention the literature. We propose a technique combining transformation, Elzaki (ET), and it equations The RLW describe ion-acoustic waves plasma...

HIV, like many other infections, is a severe and lethal infection. Fractal-fractional operators are frequently used in modeling numerous physical processes the current decade. These provide better dynamics of mathematical model because these generalization integer fractional-order operators. This paper aims to study HIV during primary infection by fractal-fractional Atangana–Baleanu (AB) The su...

We present existence and controllability results for mild solutions to the Atangana–Baleanu fractional evolution equations. prove our by applying bounded integral contractors a sequencing technique. In contrast papers available in literature, order establish results, we need not define induced inverse of operator, pertinent nonlinear function necessarily satisfy Lipschitz condition. addition, a...

In this paper, we examine the fractional order analysis of a diffusion competition spatial model describing interactions between externally introduced grey and local red squirrel under Atangana-Baleanu-Caputo (ABC) sense. Also, establish existence uniqueness population dynamics, while numerical computation is carried out using two dimensional Fractional Order Differential Transform Method (FODT...

Whooping cough, or pertussis, is an infectious disease that causes serious threats to people of all ages, specifically infant and young children, over the world. Due severe impact on health, it necessary construct a mathematical model can be used predict future dynamics disease, as well suggest strategies eliminate in optimal way. For this, we constructed new Atangana–Baleanu fractional for who...

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

This research study aims to investigate the effects of vaccination on reducing disease burden by analyzing a complex nonlinear ordinary differential equation system. The focuses five distinct sub-classes within system comprehensively explore impact vaccination. Specifically, mathematical model employed in this investigation is fractional representation tuberculosis, utilizing Atangana–Baleanu d...

Theory of fractional calculus with singular and non-singular kernels is pioneering has garnered significant interest recently. Fair amount literature on the qualitative properties differential integral equations involving different types operators available. This manuscript aims to analyze stability a class nonlinear equation in terms Atangana-Baleanu-Caputo operator. Sufficient conditions for ...