Abstract and Applied Analysis
 Journal metrics
See full report
Acceptance rate18%
Submission to final decision67 days
Acceptance to publication21 days
CiteScore1.500
Journal Citation Indicator-
Impact Factor-

Article of the Year 2021

Related Fixed Point Theorems in Partially Ordered b-Metric Spaces and Applications to Integral Equations

Read the full article

 Journal profile

Abstract and Applied Analysis publishes research with an emphasis on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimisation theory, and control theory.

 Editor spotlight

Chief Editor, Dr Wong, is an associate professor at Nanyang Technological University, Singapore. Her research interests include differential equations, difference equations, integral equations, and numerical mathematics.

 Special Issues

Do you think there is an emerging area of research that really needs to be highlighted? Or an existing research area that has been overlooked or would benefit from deeper investigation? Raise the profile of a research area by leading a Special Issue.

Latest Articles

More articles
Research Article

Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method

In this paper, we combine the Elzaki transform method (ETM) with the new homotopy perturbation method (NHPM) for the first time. This hybrid approach can solve initial value problems numerically and analytically, such as nonlinear fractional differential equations of various normal orders. The Elzaki transform method (ETM) is used to solve nonlinear fractional differential equations, and then the homotopy is applied to the transformed equation, which includes the beginning conditions. To obtain the solution to an equation, we use the inverse transforms of the Elzaki transform method (ETM). The initial conditions have a big impact on the equation’s result. We give three beginning value issues that were solved as precise or approximation solutions with high rigor to demonstrate the method’s power and correctness. It is clear that solving nonlinear partial differential equations with the crossbred approach is the best alternative.

Research Article

Asymptotics and Confluence for a Singular Nonlinear -Difference-Differential Cauchy Problem

We examine a family of nonlinear difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation difference operators, recently investigated by the author, and quasilinear Kowalevski type problems that involve contraction difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and Gevrey structure are exhibited. The other feature concerns the problem of confluence of these solutions as tends to 1.

Research Article

On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces

In this paper, we establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global implicit functions that parametrize the set of zeros of locally Lipschitz functions. Our methods rely on a nonsmooth critical point theory based on a generalization of the Ekeland variational principle.

Research Article

Measure -Pseudo-Almost Periodic Functions and Lasota-Wazewska Model with Ergodic and Unbounded Oscillating Oxygen Demand

The primary aim of this work is to introduce a new class of functions called --pseudo-almost periodic functions. Using the measure theory, we generalize in a natural way some recent works and study some properties of those --pseudo-almost periodic functions including two new composition results which play a crucial role for the existence of some --pseudo-almost periodic solutions of certain semilinear differential equations and partial differential equations. We also investigate the existence and uniqueness of the --pseudo-almost periodic solutions for some models of Lasota-Wazewska equation with measure -pseudo-almost periodic coefficient and mixed delays.

Research Article

On Certain Properties of a Univalent Function Associated with Beta Function

Beta function has some applications in differential equations and other areas of sciences and engineering where certain definite integrals are used. However, its applications to univalent functions have not been explored based on the available literature. In this work, therefore, the authors defined a univalent function associated with the beta function with . Some geometric properties of the function are discussed.

Research Article

Solutions of a Class of Multiplicatively Advanced Differential Equations II: Fourier Transforms

For a wide class of solutions to multiplicatively advanced differential equations (MADEs), a comprehensive set of relations is established between their Fourier transforms and Jacobi theta functions. In demonstrating this set of relations, the current study forges a systematic connection between the theory of MADEs and that of special functions. In a large subset of the general case, we introduce a new family of Schwartz wavelet MADE solutions for and rational with . These have all moments vanishing and have a Fourier transform related to theta functions. For low parameter values derived from , the connection of the to the theory of wavelet frames is begun. For a second set of low parameter values derived from , the notion of a canonical extension is introduced. A number of examples are discussed. The study of convergence of the MADE solution to the solution of its analogous ODE is begun via an in depth analysis of a normalized example . A useful set of generalized -Wallis formulas are developed that play a key role in this study of convergence.

Abstract and Applied Analysis
 Journal metrics
See full report
Acceptance rate18%
Submission to final decision67 days
Acceptance to publication21 days
CiteScore1.500
Journal Citation Indicator-
Impact Factor-
 Submit

Article of the Year Award: Outstanding research contributions of 2021, as selected by our Chief Editors. Read the winning articles.