Search

This study first establishes several maximum and minimum principles involving the nonlocal Monge-Ampère operator and the multi-term time-space fractional Caputo-Fabrizio derivative. Based on the maximum principle established above, on the one hand, we show that a family of multi-term time-space fractional parabolic Monge-Ampère equations has at most one solution; on the other hand, we establish some comparison principles of linear and nonlinear multi-term time-space fractional parabolic Monge-Ampère equations.

In this article, we constructed a derivative-free family of iterative techniques for extracting simultaneously all the distinct roots of a non-linear polynomial equation. Convergence analysis is discussed to show that the proposed family of iterative method has fifth order convergence. Nonlinear test models including fractional conversion, predator-prey, chemical reactor and beam designing models are included. Also many other interesting results concerning symmetric problems with application of group symmetry are also described. The simultaneous iterative scheme is applied starting with the initial estimates to get the exact roots within the given tolerance. The proposed iterative scheme requires less function evaluations and computation time as compared to existing classical methods. Dynamical planes are exhibited in CAS-MATLAB (R2011B) to show how the simultaneous iterative approach outperforms single roots finding methods that might confine the divergence zone in terms of global convergence. Furthermore, convergence domains, namely basins of attraction that are symmetrical through fractal-like edges, are analyzed using the graphical tool. Numerical results and residual graphs are presented in detail for the simultaneous iterative method. An extensive study has been made for the newly developed simultaneous iterative scheme, which is found to be efficient, robust and authentic in its domain. [ABSTRACT FROM AUTHOR]

In this paper, we provide a generating function for mix type Apostol-Genocchi polynomials of order η associated with Bell polynomials. We also derive certain important identities of Apostol Genocchi polynomials of order η based on Bell polynomials, such as the correlation formula, the implicit summation formula, the derivative formula, some correlation with Stirling numbers and their special instances. Moreover, we discover some symmetric identities and their related known results. [ABSTRACT FROM AUTHOR]

The roots of non-linear equations are a major challenge in many scientific and professional fields. This problem has been approached in a number of ways, including use of the sequential Newton's method and the traditional Weierstrass simultaneous iterative scheme. To approximate all of the roots of a given nonlinear equation, sequential iterative algorithms must use a deflation strategy because rounding errors can produce inaccurate results. This study aims to develop an efficient numerical simultaneous scheme for approximating all nonlinear equations' roots of convergence order 12. The numerical outcomes of the considered engineering problems show that, in terms of accuracy, validations, error, computational CPU time, and residual error, recently developed simultaneous methods perform better than existing methods in the literature. [ABSTRACT FROM AUTHOR]

In this article, using the principle of subordination we introduce a new class of F-like functions associated with a vertical strip domain and provided some interesting deviations or adaptation which are helpful in unification and extension of various studies of analytic functions. Furthermore, we illustrated the impact of vertical strip domain on various conic region. Inclusion relations, geometrical interpretation, coefficient estimates, inverse function coefficient estimates and solution to the Fekete-Szego problem of the defined class are discussed. Applications of our main results are given as corollaries. [ABSTRACT FROM AUTHOR]

The present study introduces a new family of analytic functions by utilizing the q-derivative operator and the q-version of the hyperbolic tangent function. We find certain inequalities, including the coefficient bounds, second Hankel determinants, and Fekete–Szegö inequalities, for this novel family of bi-univalent functions. It is worthy of note that almost all the results are sharp, and their corresponding extremal functions are presented. In addition, some special cases are demonstrated to show the validity of our findings. [ABSTRACT FROM AUTHOR]

In the present article, we define and investigate a new subfamily of holomorphic functions connected with the cosine hyperbolic function with bounded turning. Further some interesting results like sharp coefficients bounds, sharp Fekete-Szego estimate, sharp 2nd Hankel determinant and nonsharp 3rd order Hankel determinant. Moreover, the same estimates have been investigated for 2-fold, 3-fold symmetric functions, the first four initial sharp bounds of logarithmic coefficient and sharp second Hankel determinant of logarithmic coefficients fort his defined function family. [ABSTRACT FROM AUTHOR]

In this present paper, we define a new operator in conjugation with the basic (or q-) calculus. We then make use of this newly defined operator and define a new class of analytic and bi-univalent functions associated with the q-derivative operator. Furthermore, we find the initial Taylor–Maclaurin coefficients for these newly defined function classes of analytic and bi-univalent functions. We also show that these bounds are sharp. The sharp second Hankel determinant is also given for this newly defined function class. [ABSTRACT FROM AUTHOR]

In this paper, we derive some new generating functions for the products of several special numbers including (p, q)-Fibonacci numbers, (p, q)-modified Pell numbers, and (p, q)-Jacobsthal Lucas numbers. We also give some new generating functions for the products of Mersenne and Gaussian numbers with parameters p and q. [ABSTRACT FROM AUTHOR]

The study of expansions of certain mock theta functions in special functions theory has a long and quite significant history. Motivated by recent correlations between q-series and mock theta functions, we establish a new q-series transformation formula and derive the double-sum expansions for mock theta functions. As an application, we state new double-sum representations for certain mock theta functions. [ABSTRACT FROM AUTHOR]

This work is motivated essentially by the success of the applications of the nonsingular Yang–Abdel–Aty–Cattani (YAC) derivative in many research area of science, engineering, and financial mathematics. Furthermore, the major determination of this survey work is to achieve Fourier transform of the aforesaid new operator. Obviously, the Cauchy‐reaction diffusion equations have an important role in constructing well‐known models in some fields of science and engineering. Due to this motivation, we applied the aforesaid Robotnov fractional–exponential function‐based new fractional derivative to the Cauchy‐reaction diffusion equations and analyzed the proposed model analytically and graphically by using the generalized differential transform and residual power series methods. Finally, results obtained by the aforesaid proposed methods are found to be in excellent compliance with the known exact solutions. Three numerical examples are considered and described for the accuracy of the results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce mon-symbolic method to obtain the generating functions of the hybrid class of Hermite-associated Laguerre and its associated polynomials. We obtain the series definitions of these hybrid special polynomials. Also, we derive the double lacunary generating functions of the Hermite-Laguerre polynomials and the Hermite-Laguerre-Wright polynomials. Further, we find multiplicative and derivative operators for the Hermite-Laguerre-Wright polynomials which helps to find the symbolic differential equation of the Hermite-Laguerre-Wright polynomials. Some concluding remarks are also given. [ABSTRACT FROM AUTHOR]

To date, many interesting subclasses of analytic functions involving symmetrical points and other well celebrated domains have been investigated and studied. The aim of our present investigation is to make use of certain Janowski functions and a Mathieu-type series to define a new subclass of analytic (or invariant) functions. Our defined function class is symmetric under rotation. Some useful results like Fekete-Szegö functional, a number of sufficient conditions, radius problems, and results related to partial sums are derived. [ABSTRACT FROM AUTHOR]