Narrow Results

This paper proposes an effective numerical scheme for solving impulsive fractional differential equations. For this purpose, Hermite interpolation is used to approximate fractional-order integrals. The proposed methods convergence analysis is studied in detail by bounding the approximation error. Finally, the application and performance of the presented method are illustrated in two practical examples, including the impulsive control of the family of Lorenz systems, and the obtained results are compared with an existing method.

In this paper, the malaria transmission (MT) model under control strategies is considered using the Liouville–Caputo fractional order (FO) derivatives with exponential decay law and power-law. For the solutions we are using an iterative technique involving Laplace transform. We examined the uniqueness and existence (UE) of the solutions by applying the fixed-point theory. Also, fractal–fractional operators that include power-law and exponential decay law are considered. Numerical results of the MT model are obtained for the particular values of the FO derivatives $\varsigma$ and $\rho$.

In this paper, we use the techniques of fractional calculus to study the existence of a unique solution to semilinear fractional differential equation driven by a $\gamma$-Hölder continuous function $𝜃$ with $\gamma \in (\frac{2}{3},1)$. Here, the initial condition is a function that may not be defined at zero and the involved integral with respect to $𝜃$ is the extension of the Young integral [An inequality of the Hölder type, connected with Stieltjes integration, Acta Math. 67 (1936) 251–282] given by Zähle [Integration with respect to fractal functions and stochastic calculus I, Probab. Theory Related Fields 111 (1998) 333–374].

The generalization of the Chamseddine–Connes spectral triples action to its (left and right) fractional counterpart is constructed within the context of the Riemann–Liouville and Erdelyi–Kober (left and right) fractional operators. In the fractional approach, the Dirac operators is approximated by and the spectral triple is replaced by its fractional equivalent , , , 0 < α < 1. When the (left) fractional action is applied to the noncommutative space defined by the spectrum of the Standard Model, one obtains many attractive characteristics including time-dependent gauge couplings constants (), a time-dependent cosmological constant (Λ_cos), a time-dependent scalar Ricci curvature (R), a time-dependent Newton's coupling constant, and a time-dependent Higgs square mass . Furthermore, , Λ_cos, R, and were found to be nonsingulars at the Planck's time. When the (left and right) fractional bosonic action is taken into account, all the previous functions are found to be complexified, including gravity. Many additional interesting features are discussed and explored in some details.

This paper presents a fractional approach as a substitute to the integer-order model, describing the magnetohydrodynamics (MHD) effect of blood flow in a stenosed artery. We not only obtain an analytical solution for the fractional governing equation but also present an expression for the wall-shear stress. After the successful verification of our model with established models, we carry out a two-step validation with the experimental data existing in literature. Then, we analyze the obtained plots by using the analytic expression. We exhibit how fractional model (FM) is helpful for controlling the blood flow through a stenosed artery. This study also indicates that magnetic field intensity significantly controls the flow velocity and wall-shear stress to a great extent. We also show that the external magnetic field, along with the fractional order of the governing equation, plays a pivotal role in the solution of the problem involving the treatment of stenosis. Finally, we conduct some experimental data approximation by the solution to establish the credibility of the proposed fractional-order model.