Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems

Freihat, Asad; Abu-Gdairi, Radwan; Khalil, Hammad; Abuteen, Eman; Al‐Smadi, Mohammed; Khan, Rahmat Ali

doi:10.3844/ajassp.2016.501.510

Cited by 10 publications

(5 citation statements)

References 35 publications

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“…Many other researchers have studied improper integrals such as Ramanujan who presented Ramanujan's master theorem [24][25][26], which gives expressions for the Mellin transform of any continuous analytic function in terms of its Taylor expansion. The study of the application of such integrals has continued and appeared in solving integral equations, integral transforms, fractional calculus, and differential equations as well as other applications that include the procedure of computing integrals (see [27][28][29][30]).…”

Section: Introductionmentioning

confidence: 99%

General Master Theorems of Integrals with Applications

2022

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Many formulas of improper integrals are shown every day and need to be solved in different areas of science and engineering. Some of them can be solved, and others require approximate solutions or computer software. The main purpose of this research is to present new fundamental theorems of improper integrals that generate new formulas and tables of integrals. We present six main theorems with associated remarks that can be viewed as generalizations of Cauchy’s results and I.S. Gradshteyn integral tables. Applications to difficult problems are presented that cannot be solved with the usual techniques of residue or contour theorems. The solutions of these applications can be obtained directly, depending on the proposed theorems with an appropriate choice of functions and parameters.

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Section: Introductionmentioning

confidence: 99%

General Master Theorems of Integrals with Applications

2022

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“…A large number of these integrals cannot be solved manually, but they need computer software to be solved. Additionally, numerical methods can be used to solve some improper integrals that cannot be solved by previous methods [16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A Fundamental Criteria to Establish General Formulas of Integrals

Saadeh

Abu-Ghuwaleh

Qazza

et al. 2022

Journal of Applied Mathematics

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In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems, including difficult integrals with their exact solutions. The results of these problems can be obtained directly without the need for difficult calculations. New criteria for treating improper integrals are presented and illustrated in four interesting examples and some tables to simplify the procedure of using the proposed theorems. The outcomes of this study are compared with those presented by Gradshteyn and Ryzhik in the classical table of integrations. The results in this study are simple and applicable in solving integrals, and some of the well-known theorems in calculating improper integrals are considered simple cases of our research.

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“…Li et al [26] applied the method for numerical solutions of fractional Riccati differential equations. For more details see [1], [2], [11].…”

Section: Introductionmentioning

confidence: 99%

Reproducing kernel functions and homogenizing transforms

Yildirim

Akgül

2021

THERM SCI

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A lot of problems of the physical world can be modeled by nonlinear ordinary differential equations with their initial and boundary conditions. Especially higher order differential equations play a vital role in this process. The method for solution and its effectiveness are as important as the modeling. In this paper, on the basis of reproducing kernel theory, the reproducing kernel functions have been obtained for solving some nonlinear higher order differential equations. Additionally, for each problem the homogenizing transforms have been obtained.

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Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems

Cited by 10 publications

References 35 publications

General Master Theorems of Integrals with Applications

General Master Theorems of Integrals with Applications

A Fundamental Criteria to Establish General Formulas of Integrals

Reproducing kernel functions and homogenizing transforms

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