Ravi P. Agarwal
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View article: Ulam-Type Stability and Krasnosel’skii’s Fixed Point Approach for φ-Caputo Fractional Neutral Differential Equations with Iterated State-Dependent Delays
Ulam-Type Stability and Krasnosel’skii’s Fixed Point Approach for φ-Caputo Fractional Neutral Differential Equations with Iterated State-Dependent Delays Open
This work analyses the existence, uniqueness, and Ulam-type stability of neutral fractional functional differential equations with recursively defined state-dependent delays. Employing the Caputo fractional derivative of order α∈(0,1) with…
View article: Stability and numerical solutions of higher-order nonlinear time-dependent delay differential equations using Haar wavelet collocation method
Stability and numerical solutions of higher-order nonlinear time-dependent delay differential equations using Haar wavelet collocation method Open
In this paper, the authors present qualitative results for the solutions of nonlinear higher-order time-dependent delay differential equations. Proof of existence and uniqueness theorem for nth order time-dependent delay differential equat…
View article: Stability of Nonlinear Switched Fractional Differential Equations with Short Memory
Stability of Nonlinear Switched Fractional Differential Equations with Short Memory Open
Nonlinear switched systems, which combine multiple subsystems with a switching rule, have garnered significant research interest due to their complex stability properties. In this paper we consider the case where the switching times, the s…
View article: Developments in the Symmetry and Solutions to Fractional Differential Equations
Developments in the Symmetry and Solutions to Fractional Differential Equations Open
Fractional differential equations constitute an important research direction in modern mathematics and applied sciences [...]
View article: Ulam Stability for Nonlinear Fractional Differential Equations with Multi-Term and Nonlocal Multi-Point Boundary Value Problem
Ulam Stability for Nonlinear Fractional Differential Equations with Multi-Term and Nonlocal Multi-Point Boundary Value Problem Open
We focus on Ulam type stability for fractional differential equations with nonlocal multi-point and multi-term boundary conditions. The application of Ulam stability to any type of boundary condition causes some misunderstandings which are…
View article: Atypical cause of apnoea in a neonate born at 29 weeks
Atypical cause of apnoea in a neonate born at 29 weeks Open
A 29 weeks gestation, male, weighing 1270 grams was born through a vaginal delivery. He was intubated at birth and received 2 doses of surfactant. He had multiple failed extubation attempts on 1st, 7th, 28th, and 54th day of life on accoun…
View article: The Strict Stability of Impulsive Differential Equations with a Caputo Fractional Derivative with Respect to Other Functions
The Strict Stability of Impulsive Differential Equations with a Caputo Fractional Derivative with Respect to Other Functions Open
The aim of this paper is to study a nonlinear system of impulsive fractional differential equations and Caputo fractional derivatives with respect to another function (CFF). The main characteristics of these fractional derivatives are two-…
View article: New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System
New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System Open
In this work, we prove that the initial value problem for the Schrödinger–Korteweg–de Vries (SKdV) system is locally well posed in Gevrey spaces for s>−34 and k≥0. This advancement extends recent findings regarding the well posedness of th…
View article: Analysis of Mild Extremal Solutions in Nonlinear Caputo-Type Fractional Delay Difference Equations
Analysis of Mild Extremal Solutions in Nonlinear Caputo-Type Fractional Delay Difference Equations Open
This study investigates extremal solutions for fractional-order delayed difference equations, utilizing the Caputo nabla operator to establish mild lower and upper approximations via discrete fractional calculus. A new approach is employed…
View article: Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations
Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations Open
In this paper we consider impulsive delay differential equations with the Caputo fractional derivative with respect to another function on a finite interval. We set up and study a problem that consists of an initial condition on the initia…
View article: Advancements in Gevrey Regularity for a Coupled Kadomtsev–Petviashvili II System: New Insights and Findings
Advancements in Gevrey Regularity for a Coupled Kadomtsev–Petviashvili II System: New Insights and Findings Open
In this work, we prove that the initial value problem for a system of two Kadomtsev–Petviashvili II (KP II) equations coupled via both dispersive and nonlinear terms is locally well-posed in anisotropic Gevrey spaces Gs1,s2δ1,δ2,ϱ(R2)×Gs1,…
View article: An Efficient Approach for Mixed Neutral Delay Differential Equations
An Efficient Approach for Mixed Neutral Delay Differential Equations Open
In this paper, neutral delay differential equations, which contain constant and proportional terms, termed mixed neutral delay differential equations, are solved numerically. Moreover, an efficient numerical approach is introduced (a combi…
View article: Strict Stability of Fractional Differential Equations with a Caputo Fractional Derivative with Respect to Another Function
Strict Stability of Fractional Differential Equations with a Caputo Fractional Derivative with Respect to Another Function Open
In this paper, we study nonlinear systems of fractional differential equations with a Caputo fractional derivative with respect to another function (CFDF) and we define the strict stability of the zero solution of the considered nonlinear …
View article: A Computational Study on Two-Parameter Singularly Perturbed Third-Order Delay Differential Equations
A Computational Study on Two-Parameter Singularly Perturbed Third-Order Delay Differential Equations Open
A class of third-order singularly perturbed two-parameter delay differential equations of boundary value problems is studied in this paper. Regular and singular components are used to estimate the solution’s a priori bounds and derivatives…
View article: Fixed Point Theory from Early Foundations to Contemporary Challenges
Fixed Point Theory from Early Foundations to Contemporary Challenges Open
View article: Weighted Statistical Convergence and Cluster Points: The Fibonacci Sequence-Based Approach Using Modulus Functions
Weighted Statistical Convergence and Cluster Points: The Fibonacci Sequence-Based Approach Using Modulus Functions Open
In this paper, the Fibonacci sequence, renowned for its significance across various fields, its ability to illuminate numerical concepts, and its role in uncovering patterns in mathematics and nature, forms the foundation of this research.…
View article: Existence and uniqueness of the solution to initial and inverse problems for integro-differential heat equations with fractional load
Existence and uniqueness of the solution to initial and inverse problems for integro-differential heat equations with fractional load Open
This work is devoted to the unique solvability of the direct and inverse problems for a multidimensional heat equation with a fractional load in Holder spaces. In the problem under consideration, the loaded term is in the form of a fractio…
View article: Existence results for a nonlocal <i>q</i>-integro multipoint boundary value problem involving a fractional <i>q</i>-difference equation with dual hybrid terms
Existence results for a nonlocal <i>q</i>-integro multipoint boundary value problem involving a fractional <i>q</i>-difference equation with dual hybrid terms Open
This paper is devoted to the study of a fractional q -difference equation involving dual hybrid terms and equipped with nonlocal multipoint and Riemann-Liouville fractional q -integral boundary conditions. Applying a fixed point approach, …
View article: Theoretical Results on Positive Solutions in Delta Riemann–Liouville Setting
Theoretical Results on Positive Solutions in Delta Riemann–Liouville Setting Open
This article primarily focuses on examining the existence and uniqueness analysis of boundary fractional difference equations in a class of Riemann–Liouville operators. To this end, we firstly recall the general solution of the homogeneous…
View article: Efficient Study on Westervelt-Type Equations to Design Metamaterials via Symmetry Analysis
Efficient Study on Westervelt-Type Equations to Design Metamaterials via Symmetry Analysis Open
Metamaterials have emerged as a focal point in contemporary science and technology due to their ability to drive significant innovations. These engineered materials are specifically designed to couple the phenomena of different physical na…
View article: Cohen–Grossberg Neural Network Delay Models with Fractional Derivatives with Respect to Another Function—Theoretical Bounds of the Solutions
Cohen–Grossberg Neural Network Delay Models with Fractional Derivatives with Respect to Another Function—Theoretical Bounds of the Solutions Open
The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons is modeled by a Riemann–Liouville fractional derivative with respect to another function and an appropriate initial condition is set up. Some inequa…
View article: Study of Caputo fractional derivative and Riemann–Liouville integral with different orders and its application in multi‐term differential equations
Study of Caputo fractional derivative and Riemann–Liouville integral with different orders and its application in multi‐term differential equations Open
In this article, we initially provided the relationship between the RL fractional integral and the Caputo fractional derivative of different orders. Additionally, it is clear from the literature that studies into boundary value problems in…
View article: Theoretical Investigation of Fractional Estimations in Liouville–Caputo Operators of Mixed Order with Applications
Theoretical Investigation of Fractional Estimations in Liouville–Caputo Operators of Mixed Order with Applications Open
In this study, to approximate nabla sequential differential equations of fractional order, a class of discrete Liouville–Caputo fractional operators is discussed. First, some special functions are re-called that will be useful to make a co…
View article: Advanced Methods for Conformable Time-Fractional Differential Equations: Logarithmic Non-Polynomial Splines
Advanced Methods for Conformable Time-Fractional Differential Equations: Logarithmic Non-Polynomial Splines Open
In this study, we present a numerical method named the logarithmic non-polynomial spline method. This method combines conformable derivative, finite difference, and non-polynomial spline techniques to solve the nonlinear inhomogeneous time…
View article: Exploring the Landscape of Fractional-Order Models in Epidemiology: A Comparative Simulation Study
Exploring the Landscape of Fractional-Order Models in Epidemiology: A Comparative Simulation Study Open
Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. …
View article: Offset Linear Canonical Stockwell Transform for Boehmians
Offset Linear Canonical Stockwell Transform for Boehmians Open
In this article, we construct a Boehmian space using the convolution theorem that contains the offset linear canonical Stockwell transforms (OLCST) of all square-integrable Boehmians. It is also proven that the extended OLCST on square-int…
View article: Complex-Valued Suprametric Spaces, Related Fixed Point Results, and Their Applications to Barnsley Fern Fractal Generation and Mixed Volterra–Fredholm Integral Equations
Complex-Valued Suprametric Spaces, Related Fixed Point Results, and Their Applications to Barnsley Fern Fractal Generation and Mixed Volterra–Fredholm Integral Equations Open
The novelty of this work is that it is the first to introduce complex-valued suprametric spaces and apply it to Fractal Generation and mixed Volterra–Fredholm Integral Equations. In the realm of fuzzy logic, complex-valued suprametric spac…
View article: Existence of sunny nonexpansive retractions and approximation of fixed points of a representation of nonexpansive mappings
Existence of sunny nonexpansive retractions and approximation of fixed points of a representation of nonexpansive mappings Open
This paper presents an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth uniformly convex Banach space with respect to a left-regular sequence of means defined on a subset of l∞(S). The mai…
View article: Systems of First-Order Linear Fuzzy Initial Value Problems and Their Applications
Systems of First-Order Linear Fuzzy Initial Value Problems and Their Applications Open
This study primarily addresses solutions to a system of first-order linear fuzzy initial value problems in the context of granular differentiability, and explores the real-life applications of such systems.We recall the concepts of the hor…
View article: Edge of Chaos in Integro-Differential Model of Nerve Conduction
Edge of Chaos in Integro-Differential Model of Nerve Conduction Open
In this paper, we consider an integro-differential model of nerve conduction which presents the propagation of impulses in the nerve’s membranes. First, we approximate the original problem via cellular nonlinear networks (CNNs). The dynami…