We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method. We use this method for solving Generalized Time-space Fractional Schrödinger equation. The fractional derivative is described in Caputo sense. The proposed scheme finds the solution without any discritization, ...

A fractional order HIV model with both virus-tocell and cell-to-cell transmissions and therapy effect is investigated. The conditions for the existence of the equilibria are determined. Local stability analysis of the HIV model is studied by using the fractional Routh-Hurwitz stability conditions. We have generalized the integer LaSalle’s invariant theorem into fractional system and given some ...

In this study, we perform a dynamical analysis of generalized tumor model using the Caputo fractional-order derivative. Tumor growth models are widely used in biomedical research to understand dynamics development and evaluate potential treatments. The derivative is mathematical tool that recently being applied biological systems, including growth. We present detailed with examine its behavior....

Many mathematical models describe the Corona virus disease 2019 (COVID-19) outbreak; however, they require advance skills. The need for this study is to determine diffusion of COVID-19 vaccine in humans. To end, we first establish a Pythagorean fuzzy partial fractional differential equation using integral transforms express effects vaccination on humans under generalized Hukuhara conditions. We...

The present research correlates with a fuzzy hybrid approach merged homotopy perturbation transform method known as the Shehu (SHPTM). With aid of Caputo and Atangana–Baleanu under generalized Hukuhara differentiability, we illustrate reliability this scheme by obtaining fractional Cauchy reaction–diffusion equations (CRDEs) initial conditions (ICs). Fractional CRDEs play vital role in diffusio...

In this paper, a modified nonlinear Schrödinger equation with spatiotemporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled Adomian decomposition method has been defined applied to solve newly dispersion. The approximate analytical solutions are obtained compared each other graphically.

We study the existence and uniqueness of solutions for boundary value problems associated to differential equations of interval-valued functions, by using the derivative of Hukuhara and some fixed point theorems for weakly contractive mappings defined on partially ordered sets.

A fractional model of the Hopfield neural network is considered in case application generalized proportional Caputo derivative. The stability analysis this used to show reliability processed information. An equilibrium defined, which generally not a constant (different than ordinary derivatives and Caputo-type derivatives). We define exponential Mittag–Leffler equilibrium. For this, we extend s...

In this study, the meshless collocation approach is used to determine numerical solution generalized time-fractional Gardner equation. The Crank-Nicolson technique approximate space derivatives, whereas Caputo derivative of fractional order first time derivative. solutions, which show method?s efficacy and accuracy, are pro?vided discussed. shows that our method effective in producing extremely...

In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-s...