This paper proposes an innovative method that combines the homotopy analysis with Jafari transform, applying it for first time to solve systems of fractional-order linear and nonlinear differential equations. The constructs approximate solutions in form a series validates its feasibility through comparison known exact solutions. proposed approach introduces convergence parameter ℏ, which plays crucial role adjusting range solution. By appropriately selecting initial terms, speed...

<abstract><p>Multiple variants of SARS-CoV-2 have emerged but the effectiveness existing COVID-19 vaccines against has been reduced, which bring new challenges to control and mitigation pandemic. In this paper, a mathematical model for mutated with quarantine, isolation vaccination is developed studying current pandemic transmission. The basic reproduction number $ \mathscr{R}_{0} obtained. It proved that disease free equilibrium globally asymptotically stable if < 1...

In this paper, we construct an alternative proof for the long-time behavior of large-data classical solutions to 2D semi-dissipative Boussinesq equations without thermal diffusion on a bounded domain subject stress-free boundary conditions, which was previously studied in Doering et al (2018 Physica D 376/7 144–59). To demonstrate effectiveness new approach, study initial-boundary value problem related model with density variance and no-flow condition, analytic technique utilized 144–59) is...

<p style='text-indent:20px;'>This paper is devoted to the analytical study of long-time asymptotic behavior solutions Cauchy problem a system conservation laws in one space dimension, which derived from repulsive chemotaxis model with singular sensitivity and nonlinear chemical production rate. Assuming <inline-formula><tex-math id="M1">\begin{document}$ H^2 $\end{document}</tex-math></inline-formula>-norm initial perturbation around constant ground state finite using energy methods, we show...

We consider the Cauchy problem for a system of balance laws derived from chemotaxis model with singular sensitivity in multiple space dimensions. Utilizing energy methods, we first prove global well-posedness classical solutions to when only order spatial derivatives initial data is sufficiently small, and are shown converge prescribed constant equilibrium states as time goes infinity. Then that fully dissipative those corresponding partially chemical diffusion coefficient tends zero.

In this paper, we discuss a class of fractional evolution equations with the Riemann-Liouville derivative and obtain existence uniqueness mild solutions by using some classical fixed point theorem. Then give examples to demonstrate main results. MSC:30C45, 30C80.

In this paper, we study the variable-order generalized time fractional Oldroyd-B fluid model, use reduced order method and L2-1? to establish differential format with second-order accuracy, prove stability convergence of format, give numerical examples illustrate effectiveness format.

In this paper, we have established a numerical method for class of time-fractional and Riesz space distributed-order advection–diffusion equation with time-delay. Firstly, transform the derivative term diffusion into multi-term fractional derivatives by using Gauss quadrature formula. Secondly, discretize time second-order finite differences, second kind Chebyshev polynomials, convert to system algebraic equations. Finally, solve equations iterative method, prove stability convergence....

In this paper, we prove the Hyers–Ulam stability and generalized of ut(x,t)=a(t)Δu(x,t) with an initial condition u(x,0)=f(x) for x∈Rn 0&lt;t&lt;T; corresponding conclusions standard heat equation can be also derived as corollaries. All above results are proved by using properties fundamental solution equation.

This article studies the Bowen-Margulis-Sullivan (BMS) measures on non-compact manifolds without conjugate points. The finiteness of this measure unit tangent space indicates some important dynamical properties. Under assumptions uniform visibility axiom and Axiom 2, we give a criterion when BMS is finite.

This paper is concerned with the application of a hybrid collocation method to class initial value problems for differential equations fractional order. First, equation converted nonlinear Volterra integral weakly singular kernel. Then, fixed point problem. A algorithm developed solve problem, and optimal order convergence proposed obtained. Two numerical experiments are conducted demonstrate efficiency algorithm.

Most articles choose the transcendental function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>r</mml:mi><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math> to define finite Hankel transform, and very few...

The main purpose of this paper is to obtain the unique solution constant coefficient homogeneous linear fractional differential equations and nonhomogeneous if P a diagonal matrix X ( t ) ∈ C 1− q [ 0 , T ] × ]×⋯× prove existence uniqueness these two kinds for any L R m ]. Then we give examples demonstrate results.

Helical flows of generalized Maxwell fluid is researched between two infinite co-axial circular cylinders. The velocity field and the adequate shear stress corresponding to flow a with fractional derivative model, coaxial cylinders, are determined by means Laplace finite Hankel transforms. first solutions that have been obtained, presented under integral series form in terms G- R-functions, satisfy all imposed initial boundary conditions. similar for ordinary Newtonian can be also obtained...

In this paper, we discuss the existence and uniqueness of solutions for nonlinear fractional differential equations variable order with antiperiodic boundary conditions. The main results are obtained by using fixed point theorem.

&lt;abstract&gt;&lt;p&gt;By the relationship between a continuous population $ X and uniform distribution U[0, 1] $, we gain for sample quantile an equivalent expression of its variance two different quantiles asymptotic correlation coefficient. As interest can have no expectation, obtained conclusions are applicable to location estimating problem Cauchy distribution. On that occasion, finally quick effective estimator established by linear function some quantiles. For similar problems,...

The fractional stochastic vibration system is quite different from the traditional one, and its application potential enormous if noise can be deployed correctly connection between order property unlocked. This article uses a modification of well-known van der Pol oscillator with multiplicative additive recycling noises as an example to study stationary response bifurcation. First, based on principle minimum mean square error, derivative equivalent linear combination damping restoring...

The main purpose of this paper is to introduce a new integral transform named the W transform. We have been obtained some important results about At same time, relation between and other transforms has established. In order prove efficiency transform, we solved differential equations equations.

Testing judicial impartiality is a problem of fundamental importance in empirical legal studies, for which standard regression methods have been popularly used to estimate the extralegal factor effects. However, those cannot handle control variables with ultrahigh dimensionality, such as found judgment documents recorded text format. To solve this problem, we develop novel mixture conditional (MCR) approach, assuming that whole sample can be classified into number latent classes. Within each...

Basing upon the recent development of Patterson-Sullivan measures with a H\"older continuous nonzero potential function, we use tools both dynamics geodesic flows and geometric properties negatively curved manifolds to present new formula illustrating relation between exponential decay rate function corresponding critical exponent.