A method of solving a nonlinear boundary value problem with a parameter for a loaded differential equation

Dzhumabaev, D. S.; Бакирова, Е. А.; Mynbayeva, S. T.

doi:10.1002/mma.6003

Cited by 23 publications

(4 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Ары қарай параметрлеу әдісі дифференциалдық теңдеулердің әртүрлі кластары үшін шеттік есептерді шешуде Д.С. Жұмабаевтың [11,12] және оның оқушыларының жұмыстарында [13][14][15][16][17][18][19][20][21][22] орын алды.…”

Section: кіріспеunclassified

On the Unique Solvability of a Boundary Value Problem for Differential Equations With Parameter

Bakirova,

Iskakova,

Тemesheva

et al. 2024

jour

Self Cite

View full text Add to dashboard Cite

A linear boundary value problem for a differential equation with a parameter is investigated on a finite interval by the parameterization method. The studied boundary value problem with parameter is reduced to an equivalent multipoint boundary value problem with parameters by splitting the interval, introducing additional parameters at the points of splitting and new functions. The obtained equivalent boundary value problem contains Cauchy problems for ordinary differential equations with respect to new functions. By substituting the solution representation of the Cauchy problem into the boundary conditions and continuity conditions of the solution, a system of linear algebraic equations with respect to the introduced parameters is compiled. An algorithm for finding a solution to the boundary value problem with parameters is constructed. The formulation of the theorem on sufficient conditions of unique solvability of the boundary value problem with parameters is given. Sufficient conditions of its unique solvability are obtained in terms of the data of the original boundary value problem. An example showing the fulfillment of the conditions of the theorem is given.

show abstract

Section: кіріспеunclassified

On the Unique Solvability of a Boundary Value Problem for Differential Equations With Parameter

Bakirova,

Iskakova,

Тemesheva

et al. 2024

jour

Self Cite

View full text Add to dashboard Cite

show abstract

“…Currently, there are very few research findings on arbitrary fractional-order differential problems with nonlinear variables in the boundaries and infinite-point boundary value requirements. The literature [5] examines parameterized nonlinear loaded differential equations on finite intervals and suggests a technique for parameterized boundary value issue solving that relies on the solution of a nonlinear equation system. Literature [6] for multipoint boundary value problems establishes requirements for moderate solutions for linked structures involving fractional-order mixed linear equations with second-order perturbations.…”

Section: Introductionmentioning

confidence: 99%

A study of the multipoint boundary value problem for nonlinear differential equations of arbitrary fractional order based on the fixed point theorem for composite nonlinear operators

Luo

2024

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

The existence and distinctiveness of solutions, as well as the iterative approximations of the distinctive answer to the initial boundary value issue of nonlinear differential equations, may be solved with the help of the theory of nonlinear operators, which offers a strong theoretical guarantee and a fundamental tool. In this work, we examine the fixed point theory for composites nonlinear operators, which may offer a fresh approach to solving linear differential equations having arbitrary order fractional multipoint boundary value problems. The existing result of the boundary value issue’s solution is confirmed by the fixed point theorem for composites nonlinear operators, and the four-point boundary value problem for fractional-order linear equations of the Riemann-Liouville type is examined. A group of fractional-order nonlinear differential equations with deviating quantities are examined to examine the presence of an unusual positive solution for this boundary value problem. The existence of this unique positive solution is determined by the use of both the mixed monotone operator and the combined nonlinear operator fixed point theorem. Ultimately, the nonlinear Bagley-Torvik equation with a fractional order variable coefficient four-point boundary value problem is converted into a Fredholm-Hammerstein integral the formula of the second type with weakly singular or continuous kernels, and the fixed point principle is used to demonstrate the uniqueness of the solution in the space of continuous functions. Approximate solutions are provided for the second class of nonlinear Fredholm-Hammerstein integral equations with weakly singular kernels. The outcomes demonstrate the applicability and validity of the fixed point theorem to composite nonlinear operators, offering a fresh approach to solving the multipoint boundary value issue for nonlinear differential equations of any fractional order.

show abstract

“…In the present paper we propose a new approach for the study and solving of the parameter identification problem for the system of differential equations based on the Dzhumabaev's parameterization method [9][10][11][12][13][14][15][16][17][18][19][20]. The method was originally offered in [9,10] for solving two-point boundary value problems for a linear differential equation.…”

Section: Introductionmentioning

confidence: 99%

The Parameter Identification Problem for System of Differential Equations

Asanova

Шынарбек

Iskandarov³

2021

Bullet. Ser. of Phys. & Math. Sc.

View full text Add to dashboard Cite

In this paper, the parameter identification problem for system of ordinary differential equations is considered. The parameter identification problem for system of ordinary differential equations is investigated by the Dzhumabaev’s parametrization method. At first, conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations are obtained in the term of fundamental matrix of system’s differential part. Further, we establish conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations in the terms of initial data. Algorithm for finding of approximate solution to a unique solvability of the parameter identification problem for system of ordinary differential equations is proposed and the conditions for its convergence are setted. Results this paper can be use for investigating of various problems with parameter and control problems for system of ordinary differential equations. The approach in this paper can be apply to the parameter identification problems for partial differential equations.

show abstract

A method of solving a nonlinear boundary value problem with a parameter for a loaded differential equation

Cited by 23 publications

References 15 publications

On the Unique Solvability of a Boundary Value Problem for Differential Equations With Parameter

On the Unique Solvability of a Boundary Value Problem for Differential Equations With Parameter

A study of the multipoint boundary value problem for nonlinear differential equations of arbitrary fractional order based on the fixed point theorem for composite nonlinear operators

The Parameter Identification Problem for System of Differential Equations

Contact Info

Product

Resources

About