In this article, we deal with the solution of the M-Sturm Liouville problem with Bessel potential function. We use the M-Laplace transform. In this study, it is considered as an important advantage that the strong M-derivative includes the truncated Mittag-Leffler function, which allows it to be evaluated as an extended version of the classical derivative and other local derivatives. This derivative is an extremely powerful tool for generalizing complex problems. The purpose of this paper is to spy on the behavior of the spectral structure of the Bessel type M-Sturm-Liouville problem with visual analysis.
This study delves into the formulation and analysis of a novel class of polynomials, the triangle h Legendre-Laguerre polynomials, denoted as SL[h]phi (u, v, w). Through a rigorous investigation, explicit expressions and fundamental properties of these polynomials are derived. Additionally, the study establishes significant interrelations between the triangle h Legendre-Laguerre polynomials and other well-known polynomial families, thereby enhancing their relevance across diverse mathematical and scientific fields. Furthermore, the monomiality principle and symmetric identities associated with these hybrid special polynomials are systematically explored.
In this study, we develop a class of generalized fractional inequalities by employing (m, n)-polynomial (p1, p2)-convex functions defined on the coordinates. A novel integral identity for functions of two variables is established, serving as a key tool in our analysis. Furthermore, we derive new sort of Hermite-Hadamard-type inequality through generalized fractional operators. In addition, we present some new refinements of Hermite-Hadamard type inequality via (m, n)-polynomial (p1, p2)-convex functions with the help of hypergeometric functions. This framework provides a unified approach that encompasses several existing concepts, including (m, n)-polynomial harmonic convexity, (m, n)-polynomial convexity, classical harmonic convexity, and classical convexity, all obtained as specific instances of our results. Consequently, the findings presented here not only extend previously known inequalities but also recover a number of recent contributions in the literature as particular cases.
In this work, we prove the existence and uniqueness of both entropy solution and renormalized solution for an anisotropic singular parabolic ->- q-Laplacian equations using the penalization method. Moreover, we prove that the entropy solution coincide with the renormalized solution.
In this paper, the main goal is to provide sufficient conditions for the boundedness of commutators of the parabolic fractional integral operator [b, I alpha'] in parabolic total Morrey-Guliyev spaces L'p,lambda,& micro;(IIBn) with symbols b belonging to parabolic Lipschitz spaces Lambda(center dot)beta,' (IIBn).
Inverse boundary value problem for two-dimensional pseudo parabolic equation of third order with additional integral condition is considered. We first reduce our problem to some equivalent (in some sense) one. Using the Fourier method, the equivalent problem, in turn, is reduced to the system of integral equations. Then, using contraction mapping method, we prove the existence and uniqueness for the solution of the system of integral equations, which is also a unique solution of the equivalent problem. Finally, using equivalence, we prove the existence and uniqueness for the classical solution of the original problem.
In this paper we give a strong and weak type Guliyev-Spanne type boundedness criterion for the potential operator I alpha in the local generalized weighted Morrey space p,phi (Gamma, w) and the generalized weighted Morrey space Mp,phi(Gamma, w) defined on Carleson curves Gamma. For the operator I alpha we establish necessary and sufficient conditions for the p,phi (Gamma, w) and the strong and weak Guliyev-Spanne type boundedness and Mp,phi(Gamma, w).
We consider the variable-coefficient Harry Dym equation with the self-consistent source. The source consists of the variable-coefficient term and the combination of the eigenfunctions of the corresponding spectral problem for the string equation which has not spectral singularities. Assuming that the spectral problem has simple eigenvalues we apply the inverse scattering transform (IST) method and the (A, B, C) triplet technique for providing the explicit form of the multisoliton solution.
The main purpose of this work is to propose a new hybrid method to obtain analytical approximate solutions for general nonlinear time-fractional partial differential equations with inhomogeneous terms. This method is called Khalouta residual power series method (KHR,PSM) which is based on a combination of Khalouta transform method and residual power series method. The main advantage of KHR,PSM is that it does not require making any material assumptions about the problem and requires minimum computations to solve these types of equations. The analytical approximate solutions of three types of time-fractional nonlinear partial differential equations are presented by the proposed method. The obtained results are compared with the exact solutions. Through this comparison, we conclude that the proposed method is very effective and easy to apply to different types of time-fractional nonlinear partial differential equations.
In this paper, we study preservation of some mappings under the functor of G-permutation degree SPnG. We prove that if the mapping f : X-* Y is almost-open (resp., pseudo-open, monotone), then the mapping SPnGf : SPnGX-* SPnGY is also almost-open (resp., pseudo-open, monotone). In addition, we prove that the space Xn is sequential (resp., Frechet-Urysohn) if and only if the space SPnGX is sequential (resp. Frechet-Urysohn). Also, we prove that if the space Xn is strongly Frechet-Urysohn, then the space SPnGX is also a strongly Frechet-Urysohn space.
This study conducts a geometric investigation of ruled surfaces generated by the tangent, normal, and binormal unit vectors of arc-length parameterized space curves. Utilizing the N-pedal curve construction as a foundational approach, the analysis addresses fundamental geometric properties, including curvature behavior, striction curve geometry, and the distribution parameter. The proposed framework is further applied to computational geometry and geometric modeling, yielding results with relevance to both theoretical research and engineering applications. The findings establish essential geometric principles while offering practical tools for advanced modeling and analysis.
