scholarly journals On (p,q)-Analogues of Laplace-Typed Integral Transforms and Applications

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 631
Author(s):  
Sansumpan Jirakulchaiwong ◽  
Kamsing Nonlaopon ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Hwajoon Kim
Keyword(s):  
Differential Equations ◽  
Integral Transforms ◽  
Type Integral ◽  
Laplace Type

In this paper, we establish (p,q)-analogues of Laplace-type integral transforms by using the concept of (p,q)-calculus. Moreover, we study some properties of (p,q)-analogues of Laplace-type integral transforms and apply them to solve some (p,q)-differential equations.

scholarly journals Some results of Watson, Plancherel type integral transforms related to the Hartley, Fourier convolutions and applications

2021 ◽  
Author(s):  
Tuan Trinh
Keyword(s):  
Differential Equations ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Integral Transforms ◽  
System Of Differential Equations ◽  
Symmetric Form ◽  
Original Function ◽  
Type Integral ◽  
Necessary And Sufficient ◽  
Sequence Of Functions

In this work, we study the Watson-type integral transforms for the convolutions related to the Hartley and Fourier transformations. We establish necessary and sufficient conditions for these operators to be unitary in the L 2 (R) space and get their inverse represented in the conjugate symmetric form. Furthermore, we also formulated the Plancherel-type theorem for the aforementioned operators and prove a sequence of functions that converge to the original function in the defined L 2 (R) norm. Next, we study the boundedness of the operators (T k ). Besides, showing the obtained results, we demonstrate how to use it to solve the class of integro-differential equations of Barbashin type, the differential equations, and the system of differential equations. And there are numerical examples given to illustrate these.

scholarly journals New trends in Laplace type integral transforms with applications

2017 ◽  
Vol 35 (1) ◽  
pp. 173
Author(s):  
Arman Aghili
Keyword(s):  
Exact Solution ◽  
Fourier Transforms ◽  
Integral Transforms ◽  
Laplace Transforms ◽  
Two Dimensional ◽  
Stieltjes Transform ◽  
Special Series ◽  
Type Integral ◽  
Laplace Type

AbstractIn this paper, the authors provided a discussion on one and two dimensional Laplace transforms and generalized Stieltjes transform and their applications in evaluating special series and integrals. Finally, we implemented the joint Laplace – Fourier transforms to construct exact solution for a variant of the Kd.V equation. Illustrative examples are also provided.

scholarly journals Monte-Carlo for solving large linear systems of ordinary differential equations

2021 ◽  
Vol 8 (1) ◽  
pp. 37-48
Author(s):  
Sergey M. Ermakov ◽  
◽  
Maxim G. Smilovitskiy ◽  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Differential Equations ◽  
Integral Equations ◽  
Virtual Machines ◽  
Variable Coefficients ◽  
Fredholm Type ◽  
Type Integral ◽  
Constant Coefficients ◽  
Linear Differential

Monte-Carlo approach towards solving Cauchy problem for large systems of linear differential equations is being proposed in this paper. Firstly, a quick overlook of previously obtained results from applying the approach towards Fredholm-type integral equations is being made. In the main part of the paper, a similar method is being applied towards a linear system of ODE. It is transformed into an equivalent system of Volterra-type integral equations, which relaxes certain limitations being present due to necessary conditions for convergence of majorant series. The following theorems are being stated. Theorem 1 provides necessary compliance conditions that need to be imposed upon initial and transition distributions of a required Markov chain, for which an equality between estimate’s expectation and a desirable vector product would hold. Theorem 2 formulates an equation that governs estimate’s variance, while theorem 3 states a form for Markov chain parameters that minimise the variance. Proofs are given, following the statements. A system of linear ODEs that describe a closed queue made up of ten virtual machines and seven virtual service hubs is then solved using the proposed approach. Solutions are being obtained both for a system with constant coefficients and time-variable coefficients, where breakdown intensity is dependent on t. Comparison is being made between Monte-Carlo and Rungge Kutta obtained solutions. The results can be found in corresponding tables.

scholarly journals Existence of Uniqueness and Nonexistence Results of Positive Solution for Fractional Differential Equations Integral Boundary Value Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yongqing Wang
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Integral Conditions ◽  
Interesting Point ◽  
Integral Boundary ◽  
Type Integral ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
Conjugate Type

In this paper, we consider a class of fractional differential equations with conjugate type integral conditions. Both the existence of uniqueness and nonexistence of positive solution are obtained by means of the iterative technique. The interesting point lies in that the assumption on nonlinearity is closely associated with the spectral radius corresponding to the relevant linear operator.

scholarly journals Some Schemata for Applications of the Integral Transforms of Mathematical Physics

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 254 ◽  
Author(s):  
Yuri Luchko
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
First Integral ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Basic Properties ◽  
Survey Article ◽  
Laplace Integral ◽  
Generating Operators

In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed.

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