Hassan eltayeb Gadain

• PhD
• Professor (Full) at King Saud University

This study demonstrates that the Grünwald–Letnikov fractional proportional–integral–derivative (GPID) controller outperforms traditional PID controllers in adaptive cruise control systems, while conventional PID controllers struggle with nonlinearities, dynamic uncertainties, and stability, the GPID enhances robustness and provides more precise con...

In this work, nonlinear time-fractional coupled Burgers equations are solved utilizing a computational method, which is called the double and triple generalized-Laplace transform and decomposition method. We discuss the proof of triple generalized-Laplace transform for a Caputo fractional derivative. We have given four examples to show the precisio...

In this study, the solution of the (2+1)- and (3+1)-dimensional system of the time-fractional Navier–Stokes equations is gained by utilizing the triple-generalized Laplace transform decomposition method (TGLTDM) and quadruple-generalized Laplace transform decomposition method (FGLTDM). In addition, the results of the offered methods match with the...

This paper establishes a unique approach known as the multi-generalized Laplace transform decomposition method (MGLTDM) to solve linear and nonlinear dispersive KdV-type equations. This method combines the multi-generalized Laplace transform (MGLT) with the decomposition method (DM), and offers a strong procedure for handling complicated equations....

In this paper, we investigate a two-dimensional singular fractional-order parabolic partial differential equation in the Caputo sense. The partial differential equation is supplemented with Dirichlet and weighted integral boundary conditions. By employing a functional analysis method based on operator theory techniques, we prove the existence and u...

In the present article, the method which was obtained from a combination of the conformable fractional double Laplace transform method (CFDLTM) and the homotopy perturbation method (HPM) was successfully applied to solve linear and nonlinear conformable fractional partial differential equations (CFPDEs). We included three examples to help our prese...

In this article, we focus on examining the existence, uniqueness, and continuous dependence of solutions on initial data for a specific initial boundary value problem which mainly arises from one-dimensional quasi-static contact problems in nonlinear thermo-elasticity. This problem concerns a fractional nonlinear singular integro-differential equat...

The main aim of this article is to modify the space-time fractionalKdV equations using the Bessel operator. The triple Laplace transform decomposition method (TLTDM) is proposed to find the solution for a time-fractional singular KdV coupled system of equations. Three problems are discussed to check the accuracy and illustrate the effectiveness of...

In several recent studies, many researchers have shown the advantage of fractional calculus in the production of particular solutions of a huge number of linear and nonlinear partial differential equations. In this research work, different theorems related to the G-double Laplace transform (DGLT) are proved. The solution of the system of time-fract...

In this study, we employed the homotopy analysis transform method (HATM) to derive an iterative scheme to numerically solve a singular second-order hyperbolic pseudo-differential equation. We evaluated the effectiveness of the derived scheme in solving both linear and nonlinear equations of similar nature through a series of illustrative examples....

This paper establishes a novel technique, which is called the G-double-Laplace transform. This technique is an extension of the generalized Laplace transform. We study its properties with examples and various theorems related to the G-double-Laplace transform that have been addressed and proven. Finally, we apply the G-double-Laplace transform deco...

The current paper concentrates on discovering the exact solutions of the singular time-fractional Boussinesq equation and coupled time-fractional Boussinesq equation by presenting a new technique known as the double Sumudu–generalized Laplace and Adomian decomposition method. Here, two main theorems are addressed that are very useful in this work....

This research article introduces the four-dimensional natural transform Adomian decomposition method (FNADM) for solving the (3+1)-dimensional time-singular fractional coupled Burgers’ equation, along with its associated initial conditions. The FNADM approach represents a fusion of four-dimensional natural transform techniques and Adomian decomposi...

The current paper concentrates on discovering the exact solutions of the time-fractional regular and singular coupled Burger’s equations by involving a new technique known as the double Sumudu-generalized Laplace and Adomian decomposition method. Furthermore, some theorems of the double Sumudu-generalized Laplace properties are proved. Further, the...

This paper deals with a singular two dimensional initial boundary value problem for a Caputo time fractional parabolic equation supplemented by Neumann and non-local boundary conditions. The well posedness of the posed problem is demonstrated in a fractional weighted Sobolev space. The used method based on some functional analysis tools has been su...

The essential goal of this work is to suggest applying the multi-dimensional Sumdu generalized Laplace transform decomposition for solving pseudo-parabolic equations. This method is a combination of the multi-dimensional Sumudu transform, the generalized Laplace transform, and the decomposition method. We provided some examples to show the effectiv...

In this work, the time-fractional Navier–Stokes equation is discussed using a calculational method, which is called the Sumudu-generalized Laplace transform decomposition method (DGLTDM). The fractional derivatives are defined in the Caputo sense. The (DGLTDM) is a hybrid of the Sumudu-generalized Laplace transform and the decomposition method. Thr...

This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system with frictional damping terms. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary conditions. Upon some a priori estimates and density arguments, we establish the...

The two-dimensional coupled Burgers’ equation, a foundational partial differential equation, boasts widespread relevance across numerous scientific domains. Attaining precise solutions to this equation stands as a pivotal endeavor, fostering a comprehensive understanding of both physical phenomena and mathematical models. In this article, we unders...

The current study employs the natural transform decomposition method (NTDM) to test fractional-order partial differential equations (FPDEs). The present technique is a mixture of the natural transform method and the Adomian decomposition method. For the purpose of checking the precis of our technique, some examples are offered, and the series solut...

In this article, we present a numerical iterative scheme for solving a non-local singular initial-boundary value problem by combining two well known efficient methods. Namely, the homotopy analysis method and the double Laplace transform method. The resulting scheme is tested on a set of test examples to illustrate its efficiency, it generates the...

Fractional differential beam type equations are considered. By using an efficient approach, we prove the existence and uniqueness of continuous solutions. An iterative scheme for approximating the solution is given. Some examples are presented.

The coupled Burgers’ equation is a fundamental partial differential equation with applications in various scientific fields. Finding accurate solutions to this equation is crucial for understanding physical phenomena and mathematical models. While different methods have been explored, this work highlights the importance of the G-Laplace transform....

In this study, the technique established by the double Sumudu transform in combination with a new generalized Laplace transform decomposition method, which is called the double Sumudu-generalized Laplace transform decomposition method, is applied to solve general two-dimensional singular pseudo-hyperbolic equations subject to the initial conditions...

The triple Sumudu transform decomposition method (TSTDM) is a combination of the Adomian decomposition method (ADM) and the triple Sumudu transform. It is a computational method that can be appropriate for solving linear and nonlinear partial differential equations. The existence analysis of the method and partial derivatives theorems are proven. F...

The main purpose of this research paper is to discuss the solution of the singular two-dimensional pseudoparabolic equation by employing the double Sumudu-generalized Laplace transform decomposition method (DSGLTDM). We establish two theorems related to the partial derivatives. Furthermore, to investigate the relevance of the proposed method to sol...

This research work introduces a novel method called the Sumudu–generalized Laplace transform decomposition method (SGLDM) for solving linear and nonlinear non-homogeneous dispersive Korteweg–de Vries (KdV)-type equations. The SGLDM combines the Sumudu–generalized Laplace transform with the Adomian decomposition method, providing a powerful approach...

We are devoted to the study of a non-local non-homogeneous time fractional Timoshenko system with frictional and viscoelastic damping terms. We are concerned with the well-posedness of the given problem. The approach relies on some functional analysis tools, operator theory, a priori estimates and density arguments. This work can be considered as a...

We are concerned with the following semipositone Schrödinger semilinear elliptic BVP $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+qu=a+\lambda f(.,u), &{} \text {in }\Omega \text { (in the distributional sense), } \\ u>0, &{} \text {in }\Omega , \\ u=\varphi , &{} \text {on }\partial \Omega , \end{array} \right. \end{aligned}$$where \(\Ome...

This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary conditions. Upon some a priori estimates and density arguments, we establish the existence and uniqueness of t...

In this work, the exact and approximate solution for generalized linear, nonlinear, and coupled systems of fractional singular M-dimensional pseudo-hyperbolic equations are examined by using the multi-dimensional Laplace Adomian decomposition method (M-DLADM). In particular, some two-dimensional illustrative examples are provided to confirm the eff...

In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of \(\mathbb{R}^n\) (\(n\geq 2\)). The global behavior of this solution is also given.

Background: allot of teaching methods play an effective role in nursing students' gaining of competencies during their clinical rotations, Field trip is a trip by students which is designed to achieve certain objectives, cannot be achieved by using other way. Experiential learning has resulted in positive outcomes. Aim: This study aimed to assess t...

We are devoted to the study of a nonhomogeneous time-fractional Timoshenko system with frictional and viscoelastic damping terms. We are concerned with the well-posedness of the given problem. The approach relies on some functional-analysis tools, operator theory, a prori estimates, and density arguments.

In this article, several theorems of fractional conformable derivatives and triple Sumudu transform are given and proved. Based on these theorems, a new conformable triple Sumudu decomposition method (CTSDM) is intrduced for the solution of singular two-dimensional conformable functional Burger’s equation. This method is a combination of the decomp...

In this work, the solution of the linear, nonlinear, and coupled system fractional singular two-dimensional pseudo-parabolic equation is examined by using a three-dimensional Laplace Adomian decomposition method (3-DLADM). Analysis of the method is discussed, and some demonstrative examples are mentioned to confirm the power and accuracy of the rec...

The conformable double Sumudu decomposition method (CDSDM) is a combination of decomposition method (DM) and a conformable double Sumudu transform. It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been so...

In this work, the solution of the linear, nonlinear, and coupled system fractional singular two-dimensional pseudoparabolic equation is examined by using a three-dimensional Laplace Adomian decomposition method (3-DLADM). Analysis of the method is discussed, and some demonstrative examples are mentioned to confirm the power and accuracy of the reco...

The paper deals with nonlinear elliptic differential equations subject to some boundary value conditions in a regular bounded punctured domain. By means of properties of slowly regularly varying functions at zero and the Schauder fixed-point theorem, we establish the existence of a positive continuous solution for the suggested problem. Global esti...

This paper deals with the following boundary value problem where is the Riemann-Liouville fractional derivative, and the nonlinearity which could be singular at both and is required to be continuous on satisfying a mild Lipschitz assumption. Based on the Banach fixed point theorem on an appropriate space, we prove that this problem possesses a uniq...

We deal with the following Riemann–Liouville fractional nonlinear boundary value problem: $$ \textstyle\begin{cases} \mathcal{D}^{\alpha }v(x)+f(x,v(x))=0, & 2< \alpha \leq 3, x\in (0,1), \\ v(0)=v^{\prime }(0)=v(1)=0. \end{cases} $$ { D α v ( x ) + f ( x , v ( x ) ) = 0 , 2 < α ≤ 3 , x ∈ ( 0 , 1 ) , v ( 0 ) = v ′ ( 0 ) = v ( 1 ) = 0 . Under mild a...

We establish the existence, uniqueness, and positivity for the fractional Navier boundary value problem: $$\begin{aligned} \textstyle\begin{cases} D^{\alpha }(D^{\beta }\omega )(t)=h(t,\omega (t),D^{\beta }\omega (t)), & 0< t< 1, \\ \omega (0)=\omega (1)=D^{\beta }\omega (0)=D^{\beta }\omega (1)=0, \end{cases}\displaystyle \end{aligned}$$ { D α ( D...

A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary value problems for linear and nonlinear fractional and integer order differential equations in bounded domains. We present herein a collection of a priori estimates of the solution for an initial-boundary value problem for a singular fractional evolution...

In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one-and two-dimensional time-fractional Navier-Stokes problems, respectively. In order to examine the applicability of these methods, some examples are provided. The presented results confirm that the proposed met...

Abstract The present article focuses on how to find the exact solutions of the time-fractional regular and singular coupled Burgers’ equations by applying a new method that is called triple Laplace and Adomian decomposition method. Furthermore, the proposed method is a strong tool for solving many problems. The accuracy of the method is considered...

We establish the existence and qualitative behavior of positive continuous solutions to some nonlinear singular fractional differential equation in the frame of conformable fractional derivative. To this end, we combine estimates on the Green's function and a fixed point argument. Some examples are given to illustrate the applicability of our main...

We prove Hartman-type and Lyapunov-type inequalities for a class of Riemann–Liouville fractional boundary value problems with fractional boundary conditions. Some applications including a lower bound for the corresponding eigenvalue problem are obtained. 1. Introduction In [1], Lyapunov established the following striking inequality: Theorem 1. Let...

In this work, we combine conformable double Laplace transform and Adomian decomposition method and present a new approach for solving singular one-dimensional conformable pseudoparabolic equation and conformable coupled pseudoparabolic equation. Furthermore, some examples are given to show the performance of the proposed method. 1. Introduction Fr...

In this paper, we prove the existence and uniqueness of solution for some Riemann–Liouville fractional nonlinear boundary value problems. The positivity of the solution and the monotony of iterations are also considered. Some examples are presented to illustrate the main results. Our results generalize those obtained by Wei et al., (Existence and i...

The purpose of this article is to obtain the exact and approximate numerical solutions of linear and nonlinear singular conformable pseudohyperbolic equations and conformable coupled pseudohyperbolic equations through the conformable double Laplace decomposition method. Further, the numerical examples were provided in order to demonstrate the effic...

The main concern of this paper is to apply the modified double Laplace decomposition method to a singular generalized modified linear Boussinesq equation and to a singular nonlinear Boussinesq equation. An a priori estimate for the solution is also derived. Some examples are given to validate and illustrate the method.

Abstract In this study the method which was obtained from a combination of the conformable fractional double Laplace transform method and the Adomian decomposition method has been successfully applied to solve linear and nonlinear singular conformable fractional Boussinesq equations. Two examples are given to illustrate our method. Furthermore, the...

We establish new Lyapunov-type inequalities for the following conformable fractional boundary value problem ( BVP ): Tαaut+q(t)u(t)=0, a<t<b, u(a)=u′(a)=u′′(a)=u′′(b)=0, where Tαa is the conformable fractional derivative of order α∈(3,4] and q is a real-valued continuous function . Some applications to the corresponding eigenvalue problem are discu...

In the present work we introduced a new method and name it the conformable double Laplace decomposition method to solve one dimensional regular and singular conformable functional Burger’s equation. We studied the existence condition for the conformable double Laplace transform. In order to obtain the exact solution for nonlinear fractional problem...

In this work, the natural transform decomposition method (NTDM) is applied to solve the linear and nonlinear fractional telegraph equations. This method is a combined form of the natural transform and the Adomian decomposition methods. In addition, we prove the convergence of our method. Finally, three examples have been employed to illustrate the...

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable doubl...

In this work, a combined form of the double Natural transform method with the Adomian decomposition method is developed for analytic treatment of the linear and nonlinear singular one dimensional Boussinesq equations. Two examples are provided to illustrate the simplicity and relia- bility of this method. Moreover, the results show that the propose...

In this paper, we propose new technique for solving singular initial value problems of Lane-Emden type. This algorithm is based on Laplace transform and homotopy perturbation methods. The proposed scheme is shown to be accurate and tested for di§erent examples. The results obtained demonstrate the accuracy and e¢ ciency of the proposed method

In this paper, modification of double Laplace decomposition method is proposed for the analytical approximation solution of a coupled system of Burgers equation with appropriate initial conditions. Some examples are given to support the validity and applicability of the presented method.

In this paper, the modification of double Laplace decomposition method is proposed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied...

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obta...

In this article we propose a new technique, namely double Laplace decomposition method for solving nonlinear partial differential equation. The technique is described and illustrated with some examples.

In this work, the double Laplace decomposition method is applied to solve singular linear and nonlinear one-dimensional pseudohyperbolic equations. This method is based on double Laplace transform and decomposition methods. In addition, we prove the convergence of our method. This method is described and illustrated by some examples. These results...

In this paper, The Sumudu transform decomposition method is applied to solve the linear and nonlinear fractional delay differential equations (DDEs). Numerical examples are presented to support our method.

In this paper, the Adomain decomposition methods and double Laplace transform methods are combined to study linear and nonlinear singular one dimensional system of hyperbolic equations. In addition, we check the convergence of double Laplace transform decomposition method applied to our problems. Furthermore, we illustrate our proposed methods by u...

In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

In this paper, the double Laplace decomposition methods are applied to solve the non singular and singular one dimensional thermo-elasticity coupled system and. The technique is described and illustrated with some examples

In this study, we modify the Sumudu decomposition method and apply the method to study the singular initial value problems which are represented by Lane-Emden-type equations. We also consider both linear and nonlinear cases and provide some examples.

In this paper the Modified Laplace decomposition method (MLDM), is presented to obtain exact solutions for the systems of linear and nonlinear equations of Emden–Fowler type. The scheme is tested for some examples and the results demonstrate reliability and efficiency of the proposed method.

In this paper the Modified Laplace decomposition method (MLDM), is presented to obtain exact solutions for the systems of linear and nonlinear equations of Emden–Fowler type. The scheme is tested for some examples and the results demonstrate reliability and efficiency of the proposed method.

It is well known that the methods connected to the employment of integral transforms are very useful in mathematical analysis. Those methods are successfully applied (i) to solve differential and integral equations, (ii) to study special functions, (iii) to compute integrals. In this special issue we publish many articles of the highest quality. Th...

In this study we develop sufficient condition in order to determine the solution of delay differential equation is oscillatory or not oscillatory further we also obtain a polynomial approximation to determine the stability of the solutions.

We develop a method to obtain approximate solutions for nonlinear systems of Volterra integrodifferential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled Volterra integrodifferential equations. The nonlinear term can easily be handled with the help of A...

Double Laplace transform method was applied to evaluate the exact value of double infinite series. Further we generalize the current existing methods and provide some examples to illustrate and verify that the present method is a more general technique.

Double differential transform method has been employed to compute double Laplace transform. To illustrate the method, four examples of different forms have been prepared.

Double Laplace transform is applied to solve general linear telegraph and partial integrodifferential equations. The scheme is tested through some examples, and the results demonstrate reliability and efficiency of the proposed method.

The editors would like to express their gratitude to all the authors for their contribution and collaboration and to the many reviewers who were involved in the reviewing process and for their valuable comments, suggestions, and timely reports. Further we also acknowledge the assistance and help which were provided by the editorial board members of...

The properties of the multiple Laplace transform and convolutions on a time scale are studied. Further, some related results are also obtained by utilizing the double Laplace transform. We also provide an example in order to illustrate the main result.

Purpose Our aim in this study is to generate some partial differential equations (PDEs) with variable coefficients by using the PDEs with non-constant coefficients. Methods Then by applying the single and double convolution products, we produce some new equations having polynomials coefficients. We then classify the new equations on using the clas...

We develop a method to obtain approximate solutions of nonlinear system of partial differential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials...

We study the relationship between Sumudu and Laplace transforms and further make some comparison on the solutions. We provide some counterexamples where if the solution of differential equations exists by Laplace transform, the solution does not necessarily exist by using the Sumudu transform; however, the examples indicate that if the solution of...

The Sumudu transform of certain elementary matrix functions is obtained. These transforms are then used to solve the differential equation of a general linear conservative vibration system, a vibrating system with a special type of viscous damping.

In this paper we consider linear second order partial differential equations with constant coefficients; then by using the single and double convolution products we produce some new equations with variable coefficients and we classify the new equations. It is shown that the classifications of the new equations are similar to the original equations...

In this study we apply convolution and tensor products of distribution to solve the non-homogenous wave equation with initial condition and discuss the uniqueness and continuity of solution. We also show that the tensor product can be applied to compute the some singular integrals.

In this paper, we discuss the existence of double Sumudu transform and study relationships between Laplace and Sumudu transforms. Further, we apply two transforms to solve linear ordi-nary differential equations with constant coefficients and non con-stant coefficients.

In this paper we give some remark about the relationship between Sumudu and Laplace transforms, further; for the comparison purpose, we apply both transforms to solve partial differential equations to see the differences and similarities.

In this paper, we study boundary value problems for a mixed–type differential equation. The existence and uniqueness of generalized solution is proved. The proof is based on an energy inequality and density of the range

In this study we consider further analysis on the classification problem of linear second order partial differential equations with non-constant coefficients. The equations are produced by using convolution with odd or even functions. It is shown that the patent of classification of new equations is similar to the classification of the original equ...

Integral transform method is widely used to solve the several differential equations with the initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform was introduced as a new integral transform by Watugala to solve some ordinary differential equations in control engineering. Later, i...

In this paper, we study the properties of Sumudu transform and relationship between Laplace and Sumudu transforms. Further, we also provide an example of the double Sumudu transform in order to solve the wave equation in one dimension which is having singularity at initial conditions.

In this paper, we generalize the concepts of a new integral transform, namely the Sumudu transform, to distributions and study some of their properties. Further, we also apply this transform to solve one-dimensional wave equation having a singularity at the initial conditions.

The regular system of differential equations with convolution terms solved by Sumudu transform.

In this study, we apply double integral transforms to solve partial differential equation namely double Laplace and Sumudu transforms, in particular the wave and poisson's equations were solved by double Sumudu transform and the same result can be obtained by double Laplace transform.

In this work a new integral transform, namely Sumudu transform was applied to solve linear ordinary differential equation with and without constant coefficients having convolution terms. In particular we apply Sumudu transform technique to solve Spring-Mass systems, Population Growth and financial problem.