Vol. 31 No. 1 (2024)

Open Access

Articles

Article ID: 2424

SOLVING A FRACTIONAL EVOLUTION EQUATION IN THE SENSE OF CAPUTO-HADAMARD WITH CAUCHY AND BOUNDARY CONDITIONS BY SBA METHOD

by Germain KABORE, Bakari Abbo, Windjiré SOME, Ousséni SO, Blaise SOME

Advances in Differential Equations and Control Processes, Vol.31, No.1, 2024;

Exact solutions of fractional evolution equations in the sense of Caputo-Hadamard with Cauchy and boundary conditions are obtained by employing the SBA method.

Open Access

Articles

Article ID: 2425

DEVELOPING ANSATZ METHOD FOR SOLVING THE NEUTRON DIFFUSION SYSTEM UNDER GENERAL PHYSICAL CONDITIONS

by Tami M. T. Alsubie, Abdelhalim Ebaid, Amjad S. S. Albalawi, Saeed A.Alghamdi, Fawzi F. M. Alhamdi, Omar S. H. Alhamd, Salman M. M. Al-Anzi, Mona Aljoufi

Advances in Differential Equations and Control Processes, Vol.31, No.1, 2024;

This paper develops an ansatz method to derive the analytic solution of the neutron flux system under general initial conditions. Explicit closed series forms are established for the neutron flux and the delayed neutron concentration in terms of exponential functions. Existing results in the literature are recovered as special cases.

Open Access

Articles

Article ID: 2426

AN EFFICIENT SCHEME TO SOLVE FOURTH ORDER NONLINEAR TRIPLY SINGULAR FUNCTIONAL DIFFERENTIAL EQUATION

by A. H. Tedjani, Mahmoud M. Abdelwahab, M. A. Abdelkawy

Advances in Differential Equations and Control Processes, Vol.31, No.1, 2024;

We present a novel mathematical model based on the fourth order multi-singular nonlinear functional differential equations. This designed nonlinear functional model has singularities at three points, making the model more complicated and harder in nature. The delayed and multi-prediction terms in the model clearly represent the functionality of the model. Three different variants of the novel nonlinear triply singular functional differential model have been presented and the numerical results of each variant are obtained by using a well-known spectral collocation technique. For the perfection and excellence of the designed mathematical nonlinear model, the obtained numerical results of each variant have been compared with the exact solutions.

Open Access

Articles

Article ID: 2427

SUMUDU AND ELZAKI INTEGRAL TRANSFORMS FOR SOLVING SYSTEMS OF INTEGRAL AND ORDINARY DIFFERENTIAL EQUATIONS

by Mohammad Almousa, Ahmad Al-Hammouri, Qutebah Ali Almomani, Mustafa Husam Alomari, Mustafa Mohammad Alzubaidi

Advances in Differential Equations and Control Processes, Vol.31, No.1, 2024;

We present two integral transforms namely Sumudu (ST) and Elzaki (ET) transforms for solving systems of integral and ordinary differential equations. Also, we study some properties of these transforms. The presented integral transforms are new and simple for solving problems in systems of integral equations and ordinary differential equations. Some examples were successfully solved using these integral transforms. The obtained results reveal that the two integral transforms are effective.

Open Access

Articles

Article ID: 2428

HIGHER FRACTIONAL ORDER $p$-LAPLACIAN BOUNDARY VALUE PROBLEM AT RESONANCE ON AN UNBOUNDED DOMAIN

by Ezekiel K. Ojo, Samuel A. Iyase, Timothy A. Anake

Advances in Differential Equations and Control Processes, Vol.31, No.1, 2024;

In this work, we use the Ge and Ren extension of Mawhin's coincidence degree theory to investigate the solvability of the $p$-Laplacian fractional order boundary value problem of the form $$ \begin{aligned} & \left(\phi_p\left(D_{0+}^\alpha x(t)\right)\right)^{\prime} \\ = & f\left(t, x(t), D_{0+}^{\alpha-3} x(t), D_{0+}^{\alpha-2} x(t), D_{0+}^{\alpha-1} x(t), D_{0+}^\alpha x(t)\right), \quad t \in(0,+\infty), \\ & x(0)=0=D_{0+}^{\alpha-3} x(0), \quad D_{0+}^{\alpha-2} x(0)=\int_0^1 D_{0+}^{\alpha-2} x(t) d A(t), \\ & \lim _{t \rightarrow+\infty} D_{0+}^{\alpha-1} x(t)=\sum_{i=1}^m \mu_i D_{0+}^{\alpha-1} x\left(\xi_i\right), \quad D_{0+}^\alpha x(\infty)=0, \end{aligned} $$ where $3<\alpha \leq 4$. The conditions $\int_0^1 d A(t)=1, \quad \int_0^1 t d A(t)=0$, $\sum_{i=1}^m \mu_i=1$ and $\sum_{i=1}^m \mu_i \xi_i^{-1}=0$ are critical for resonance.

Open Access

Articles

Article ID: 2429

ADOMIAN’S METHOD FOR SOLVING A NONLINEAR EPIDEMIC MODEL

by Amjad A. Alsubaie, Mona D. Aljoufi, Abdullah G. S. Alotaibi, Ahmad S. S. Alfaydi, Rana M. Alyoubi, Bushra A. M. Aljuhani, Ebtesam F. S. Alsahli, Badriah S. Alanazi

Advances in Differential Equations and Control Processes, Vol.31, No.1, 2024;

This paper solves the susceptible-infected-recovered (SIR) model by means of the Adomian decomposition method (ADM). The ADM provides series solutions for the infected and recovered individuals. Such series solutions transform to exact ones under certain constraints of the initial conditions. In addition, closed form solutions are obtained for the infected and recovered individuals by rearranging the components of the ADM series. The accuracy is examined via comparing our results with an accurate numerical method. Agreement between our results and those of the numerical method is achieved.

Open Access

Articles

Article ID: 2430

ON 3D COMPRESSIBLE PRIMITIVE EQUATIONS APPROXIMATION OF ANISOTROPIC NAVIER-STOKES EQUATIONS: RIGOROUS JUSTIFICATION

by Jules Ouya, Arouna Ouedraogo

Advances in Differential Equations and Control Processes, Vol.31, No.1, 2024;

In this paper, we obtain the 3D compressible primitive equations approximation without gravity by taking the small aspect ratio limit to the Navier-Stokes equations in the isothermal case with gravity. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in general large scale geophysical motions that the vertical scale is significantly smaller than horizontal. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations to the compressible primitive equations. In addition to the presence of gravity, we consider that the viscosity of the fluid depends on its density and that it is submitted to a quadratic friction force.