scholarly journals A new class of Appell-type Changhee-Euler polynomials and related properties

2021 ◽  
Vol 6 (12) ◽  
pp. 13566-13579
Author(s):  
Tabinda Nahid ◽  
◽  
Mohd Saif ◽  
Serkan Araci ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Generating Function ◽  
Graphical Representations ◽  
Euler Polynomials ◽  
New Class ◽  
New Type ◽  
Changhee Polynomials

<abstract><p>A remarkably large number of polynomials and their extensions have been presented and studied. In the present paper, we introduce the new type of generating function of Appell-type Changhee-Euler polynomials by combining the Appell-type Changhee polynomials and Euler polynomials and the numbers corresponding to these polynomials are also investigated. Certain relations and identities involving these polynomials are established. Further, the differential equations arising from the generating function of the Appell-type Changhee-Euler polynomials are derived. Also, the graphical representations of the zeros of these polynomials are explored for different values of indices.</p></abstract>

scholarly journals A New Class of Hermite-Apostol Type Frobenius-Euler Polynomials and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 652
Author(s):  
Serkan Araci ◽  
Mumtaz Riyasat ◽  
Shahid Wani ◽  
Subuhi Khan
Keyword(s):  
Generating Function ◽  
Zeta Functions ◽  
Euler Polynomials ◽  
Power Sums ◽  
New Class ◽  
Summation Formulae ◽  
Special Cases ◽  
Hybrid Class

The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite–Apostol-type Frobenius–Euler polynomials, and to characterize their properties via different generating function techniques. Several explicit relations involving Hurwitz–Lerch Zeta functions and some summation formulae related to these polynomials are derived. Further, we establish certain symmetry identities involving generalized power sums and Hurwitz–Lerch Zeta functions. An operational view for these polynomials is presented, and corresponding applications are given. The illustrative special cases are also mentioned along with their generating equations.

scholarly journals VII. On the theory of definite integrals

1855 ◽  
Vol 145 ◽  
pp. 157-178
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Definite Integrals ◽  
New Class ◽  
Factorial Series ◽  
New Type ◽  
Lagrange's Series ◽  
Linear Differential ◽  
Almost All

I PROPOSE in the following paper to investigate some new methods for summing various kinds of series, including almost all of the more important which are met with in analysis, by means of definite integrals, and to apply the same to the evaluation of a large number of definite integrals. In a paper which appeared in the Cambridge and Dublin Mathematical Journal for May 1854, I applied certain of these series to the integration of linear differential equations by means of definite integrals. Now Professor Boole has shown, in an admirable memoir which appeared in the Philosophical Transactions for the year 1844, that the methods which he has invented for the integration of linear differential equations in finite terms, lead to the summation of numerous series of an exactly similar nature, whence it follows that the combination of his methods of summation with mine, will lead to the evaluation of a large number of definite integrals, as will be shown in this paper. It is hence evident that the discovery of other modes of summing these series by means of definite integrals must in all cases lead to the evaluation of new groups of definite integrals, as will also be shown in the following pages. I then point out that these investigations are equivalent to finding all the more important definite integrals whose values can be obtained in finite terms by the solution of linear differential equations with variable coefficients. Again, there are certain algebraical equations which can be solved at once by Lagrange’s series, and by common algebraical processes; the summation of the former by means of definite integrals affords us a new class of results, which I next consider. A continental mathematician, M. Smaasen , has given, in a recent volume of Crelle’s Journal, certain methods of combining series together which give us the means of reducing various multiple integrals to single ones. The series hitherto considered are what have been denominated factorial series” ; but, lastly, I proceed to show that analogous processes extend to series of a very complicated nature and of an entirely different form, and for that purpose sum by means of definite integrals certain series whose values are obtained in finite terms in the ' Exercices des Mathématiques ’ by means of the Residual Calculus. The total result will be the evaluation of an enormous number of definite integrals on an entirely new type, and the application of definite integrals to the summation of many intricate series.

scholarly journals A class of orthogonal polynomials of a new type

1983 ◽  
Vol 6 (1) ◽  
pp. 171-180
Author(s):  
M. Dutta ◽  
Kanchan Prabha Manocha
Keyword(s):  
Positive Integer ◽  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Generating Function ◽  
Recurrence Relations ◽  
Variable Parameter ◽  
Negative Integer ◽  
Special Cases ◽  
New Type ◽  
Fixed Positive Integer

The purpose of this paper is to study a class of polynomialsFnm(x,λ,ν)associated with a class ofmdifferential equations, whereλis fixed,nis a variable parameter,mis fixed positive integer andνis a non-negative integer<m. We also obtain all the important properties of this class of polynomials including Rodrigues' formulas, generating function, and recurrence relations. Several special cases of interest are obtained from our analysis.

Theoretical and experimental research on slip and uplift of the timber-concrete composite beam

BioResources ◽  
2020 ◽  
Vol 15 (3) ◽  
pp. 7079-7099
Author(s):  
Jianying Chen ◽  
Guojing He ◽  
Xiaodong (Alice) Wang ◽  
Jiejun Wang ◽  
Jin Yi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Deformation Theory ◽  
Concrete Slab ◽  
Theoretical Calculations ◽  
Structural Element ◽  
Structural Efficiency ◽  
Theoretical Investigations ◽  
New Type ◽  
Interlayer Slip ◽  
Good Agreement

Timber-concrete composite beams are a new type of structural element that is environmentally friendly. The structural efficiency of this kind of beam highly depends on the stiffness of the interlayer connection. The structural efficiency of the composite was evaluated by experimental and theoretical investigations performed on the relative horizontal slip and vertical uplift along the interlayer between composite’s timber and concrete slab. Differential equations were established based on a theoretical analysis of combination effects of interlayer slip and vertical uplift, by using deformation theory of elastics. Subsequently, the differential equations were solved and the magnitude of uplift force at the interlayer was obtained. It was concluded that the theoretical calculations were in good agreement with the results of experimentation.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

scholarly journals A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 648
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran ◽  
Deena Al-Kadi
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
New Class

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 174
Author(s):  
Janez Urevc ◽  
Miroslav Halilovič
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Integral Form ◽  
Collocation Methods ◽  
Nonlinear Odes ◽  
New Class ◽  
New Methods ◽  
Runge Kutta

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.

scholarly journals New type of degenerate Daehee polynomials of the second kind

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sunil Kumar Sharma ◽  
Waseem A. Khan ◽  
Serkan Araci ◽  
Sameh S. Ahmed
Keyword(s):  
Generating Function ◽  
Special Class ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Higher Order ◽  
Bernoulli Numbers And Polynomials ◽  
New Type ◽  
Order Degenerate ◽  
Math Phys

Abstract Recently, Kim and Kim (Russ. J. Math. Phys. 27(2):227–235, 2020) have studied new type degenerate Bernoulli numbers and polynomials by making use of degenerate logarithm. Motivated by (Kim and Kim in Russ. J. Math. Phys. 27(2):227–235, 2020), we consider a special class of polynomials, which we call a new type of degenerate Daehee numbers and polynomials of the second kind. By using their generating function, we derive some new relations including the degenerate Stirling numbers of the first and second kinds. Moreover, we introduce a new type of higher-order degenerate Daehee polynomials of the second kind. We also derive some new identities and properties of this type of polynomials.

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