Modeling the Dependence of Atmospheric Pressure with Altitude using Caputo and Caputo-Fabrizio Fractional Derivatives

This article is concerned with the model describes the relationship between the atmospheric pressure with altitude by converting the ordinary initial value problems (classical model) to fractional value problems involving Caputo and Caputo-Fabrizio fractional derivatives of real order. We investigate the existence and uniqueness of the proposed fractional model when Caputo-Fabrizio derivative is used. The aim is to show, based on experimental data from a real experiment and by using the root-mean-square deviation technique that the fractional approach may lead to a better estimation for the parameters than the ordinary one. A comparison between the error rates of the classical, Caputo, and Caputo-Fabrizio is also introduced

Existence results by Mönch's fixed point theorem for a tripled system of sequential fractional differential equations

In this paper, we study the existence of the solutions for a tripled system of Caputo sequential fractional differential equations. The main results are established with the aid of Mönch's fixed point theorem. The stability of the tripled system is also investigated via the Ulam-Hyer technique. In addition, an applied example with graphs of the behaviour of the system solutions with different fractional orders are provided to support the theoretical results obtained in this study

Mathematical analysis and numerical simulations of the piecewise dynamics model of Malaria transmission: A case study in Yemen

This study presents a mathematical model capturing Malaria transmission dynamics in Yemen, incorporating a social hierarchy structure. Piecewise Caputo-Fabrizio derivatives are utilized to effectively capture intricate dynamics, discontinuities, and different behaviors. Statistical data from 2000 to 2021 is collected and analyzed, providing predictions for Malaria cases in Yemen from 2022 to 2024 using Eviews and Autoregressive Integrated Moving Average models. The model investigates the crossover effect by dividing the study interval into two subintervals, establishing existence, uniqueness, positivity, and boundedness of solutions through fixed-point techniques and fractional-order properties of the Laplace transformation. The basic reproduction number is computed using a next-generation technique, and numerical solutions are obtained using the Adams-Bashforth method. The results are comprehensively discussed through graphs. The obtained results can help us to better control and predict the spread of the disease

A Novel Implementation of Dhage’s Fixed Point Theorem to Nonlinear Sequential Hybrid Fractional Differential Equation

In this work, the existence and uniqueness of solutions to a sequential fractional (Hybrid) differential equation with hybrid boundary conditions were investigated by the generalization of Dhage’s fixed point theorem and Banach contraction mapping, respectively. In addition, the U-H technique is employed to verify the stability of this solution. This study ends with two examples illustrating the theoretical findings

On the Controllability of Conformable Fractional Deterministic Control Systems in Finite Dimensional Spaces

In this paper, we establish a set of convenient conditions of controllability for semilinear fractional finite dimensional control systems involving conformable fractional derivative. Indeed, sufficient conditions of controllability for a semilinear conformable fractional system are presented, assuming that the corresponding linear systems are controllable. The present method is based on conformable fractional exponential matrix, Gramian matrix, and the iterative technique. Two illustrated examples are carried out to establish the facility and efficiency of this technique

Existence and Ulam–Hyers Stability Results for a System of Coupled Generalized Liouville–Caputo Fractional Langevin Equations with Multipoint Boundary Conditions

We study the existence and uniqueness of solutions for coupled Langevin differential equations of fractional order with multipoint boundary conditions involving generalized Liouville–Caputo fractional derivatives. Furthermore, we discuss Ulam–Hyers stability in the context of the problem at hand. The results are shown with examples. Results are asymmetric when a generalized Liouville–Caputo fractional derivative (ρ) parameter is changed

Fractional Stochastic Integro-Differential Equations with Nonintantaneous Impulses: Existence, Approximate Controllability and Stochastic Iterative Learning Control

In this paper, existence/uniqueness of solutions and approximate controllability concept for Caputo type stochastic fractional integro-differential equations (SFIDE) in a Hilbert space with a noninstantaneous impulsive effect are studied. In addition, we study different types of stochastic iterative learning control for SFIDEs with noninstantaneous impulses in Hilbert spaces. Finally, examples are given to support the obtained results

Relative Controllability and Ulam–Hyers Stability of the Second-Order Linear Time-Delay Systems

We introduce the delayed sine/cosine-type matrix function and use the Laplace transform method to obtain a closed form solution to IVP for a second-order time-delayed linear system with noncommutative matrices A and Ω. We also introduce a delay Gramian matrix and examine a relative controllability linear/semi-linear time delay system. We have obtained the necessary and sufficient condition for the relative controllability of the linear time-delayed second-order system. In addition, we have obtained sufficient conditions for the relative controllability of the semi-linear second-order time-delay system. Finally, we investigate the Ulam–Hyers stability of a second-order semi-linear time-delayed system

Relative Controllability and Ulam–Hyers Stability of the Second-Order Linear Time-Delay Systems

We introduce the delayed sine/cosine-type matrix function and use the Laplace transform method to obtain a closed form solution to IVP for a second-order time-delayed linear system with noncommutative matrices A and Ω. We also introduce a delay Gramian matrix and examine a relative controllability linear/semi-linear time delay system. We have obtained the necessary and sufficient condition for the relative controllability of the linear time-delayed second-order system. In addition, we have obtained sufficient conditions for the relative controllability of the semi-linear second-order time-delay system. Finally, we investigate the Ulam–Hyers stability of a second-order semi-linear time-delayed system

A Novel Three-Step Numerical Solver for Physical Models under Fractal Behavior

In this paper, we suggest an iterative method for solving nonlinear equations that can be used in the physical sciences. This response is broken down into three parts. Our methodology is inspired by both the standard Taylor’s method and an earlier Halley’s method. Three evaluations of the given function and two evaluations of its first derivative are all that are needed for each iteration with this method. Because of this, the unique methodology can complete its goal far more quickly than many of the other methods currently in use. We looked at several additional practical research models, including population growth, blood rheology, and neurophysiology. Polynomiographs can be used to show the convergence zones of certain polynomials with complex values. Polynomiographs are produced as a byproduct, and these end up having an appealing look and being artistically engaging. The twisting of polynomiographs is symmetric when the parameters are all real and asymmetric when some of the parameters are imaginary