Rohul Amin
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View article: Implications for optimizing treatment timing: day of week variation in PTSD symptom clusters
Implications for optimizing treatment timing: day of week variation in PTSD symptom clusters Open
Introduction Posttraumatic stress disorder (PTSD) has four symptom clusters: intrusion, avoidance, negative cognitions/mood, and hyperarousal. Little is known about day-to-day variation in the symptom clusters. If there is such variation, …
View article: INVESTIGATING JERK PHENOMENON BY USING FRACTAL-FRACTIONAL ANALYSIS
INVESTIGATING JERK PHENOMENON BY USING FRACTAL-FRACTIONAL ANALYSIS Open
Fractal-fractional calculus has attracted much attention in the last few years due to its wide range applications in various disciplines of science and technology. The class of differential equations with order lying in [Formula: see text]…
View article: Daily Variation in Posttraumatic Stress Disorder Symptom Clusters in Individuals with and without Posttraumatic Stress Disorder
Daily Variation in Posttraumatic Stress Disorder Symptom Clusters in Individuals with and without Posttraumatic Stress Disorder Open
Background: Posttraumatic stress disorder (PTSD) has four symptom clusters: intrusion, avoidance, negative cognitions/mood, and hyperarousal. Little is known about day-to-day variation in the four PTSD symptom clusters. This study examined…
View article: Hybrid Haar wavelet and meshfree methods for hyperbolic double interface problems: Numerical implementations and comparative performance analysis
Hybrid Haar wavelet and meshfree methods for hyperbolic double interface problems: Numerical implementations and comparative performance analysis Open
This paper introduces a variety of approaches for solving 2D and 3D hyperbolic double interface problems. The methods are based on the Haar wavelet method, multiquadric radial basis function method, and integrated multiquadric radial basis…
View article: Haar wavelet collocation technique for numerical solution of porous media equations
Haar wavelet collocation technique for numerical solution of porous media equations Open
This paper focuses on using efficient Haar wavelet collocation method to nonlinear parabolic differential equations in order to solve steady state pore-scale creeping fluid flow in porous medium, substituting finite Haar series for space d…
View article: THEORETICAL ANALYSIS AND NUMERICAL SOLUTION OF LINEAR AND NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
THEORETICAL ANALYSIS AND NUMERICAL SOLUTION OF LINEAR AND NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS Open
In this paper, a collocation method based on the Haar wavelet is presented for the solution of both linear and nonlinear first-order neutral delay differential equations. The Haar functions are used to approximate the first-order derivativ…
View article: On existence and numerical solution of higher order nonlinear integro-differential equations involving variable coefficients
On existence and numerical solution of higher order nonlinear integro-differential equations involving variable coefficients Open
We investigate the approximate solution to a class of fourth-order Volterra–Fredholm integro differential equations (VFIDEs). Additionally, we are able to get some adequate results for the existence of a solution with the use of nonlinear …
View article: A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques
A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques Open
In this paper, a new spatio-temporal model is formulated to study the spread of coronavirus infection (COVID-19) in a spatially heterogeneous environment with the impact of vaccination. Initially, a detailed qualitative analysis of the spa…
View article: A computational algorithm for solving linear fractional differential equations of variable order
A computational algorithm for solving linear fractional differential equations of variable order Open
An algorithm for solving a class of linear variable-order fractional differential equations (FDEs) numerically is presented in this paper. We utilized a combination of Caputo fractional derivatives with the Haar wavelet collocation method …
View article: A HYBRID NUMERICAL TECHNIQUE FOR SOLVING THREE-DIMENSIONAL SECOND-ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
A HYBRID NUMERICAL TECHNIQUE FOR SOLVING THREE-DIMENSIONAL SECOND-ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS Open
In this paper, a hybrid approach is presented for the numerical solution of three-dimensional parabolic partial differential equations. This new approach is applicable to both linear and nonlinear parabolic problems including systems. This…
View article: EXISTENCE AND SOLUTION OF THIRD-ORDER INTEGRO-DIFFERENTIAL EQUATIONS VIA HAAR WAVELET METHOD
EXISTENCE AND SOLUTION OF THIRD-ORDER INTEGRO-DIFFERENTIAL EQUATIONS VIA HAAR WAVELET METHOD Open
This paper is related to some qualitative results about the existence and uniqueness of a solution to a third-order problem by using a fixed point approach. Haar technique is applied for numerical solution of a third-order linear integro-d…
View article: NUMERICAL SOLUTIONS OF NONLINEAR DELAY INTEGRO-DIFFERENTIAL EQUATIONS USING HAAR WAVELET COLLOCATION METHOD
NUMERICAL SOLUTIONS OF NONLINEAR DELAY INTEGRO-DIFFERENTIAL EQUATIONS USING HAAR WAVELET COLLOCATION METHOD Open
In this paper, Haar wavelet collocation method (HWCM) for nonlinear delay Volterra, delay Fredholm and delay Volterra–Fredholm Integro-Differential Equations (IDEs) are studied numerically using HWCM. This method is very useful for solving…
View article: EXTENSION OF HAAR WAVELET TECHNIQUES FOR MITTAG-LEFFLER TYPE FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
EXTENSION OF HAAR WAVELET TECHNIQUES FOR MITTAG-LEFFLER TYPE FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS Open
Fractional order integro-differential equation (FOIDE) of Fredholm type is considered in this paper. The mentioned equations have many applications in mathematical modeling of real world phenomenon like image and signal processing. Keeping…
View article: Two-dimensional Haar Wavelet Method for Numerical Solution of Delay Partial Differential Equations
Two-dimensional Haar Wavelet Method for Numerical Solution of Delay Partial Differential Equations Open
In this paper, a two-dimensional Haar wavelet collocation method is applied to obtain the numerical solution of delay and neutral delay partial differential equations. Both linear and nonlinear problems can be solved using this method. Som…
View article: Efficient Numerical Scheme for the Solution of HIV Infection CD4+ T-Cells Using Haar Wavelet Technique
Efficient Numerical Scheme for the Solution of HIV Infection CD4+ T-Cells Using Haar Wavelet Technique Open
In this paper, Haar collocation algorithm is developed for the solution of first-order of HIV infection CD4+ T-Cells model. In this technique, the derivative in the nonlinear model is approximated by utilizing Haar functions. The value of …
View article: Haar wavelet method for solution of variable order linear fractional integro-differential equations
Haar wavelet method for solution of variable order linear fractional integro-differential equations Open
In this paper, we developed a computational Haar collocation scheme for the solution of fractional linear integro-differential equations of variable order. Fractional derivatives of variable order is described in the Caputo sense. The give…
View article: THEORETICAL AND COMPUTATIONAL RESULTS FOR MIXED TYPE VOLTERRA–FREDHOLM FRACTIONAL INTEGRAL EQUATIONS
THEORETICAL AND COMPUTATIONAL RESULTS FOR MIXED TYPE VOLTERRA–FREDHOLM FRACTIONAL INTEGRAL EQUATIONS Open
In this paper, we develop a numerical method for the solutions of mixed type Volterra–Fredholm fractional integral equations (FIEs). The proposed algorithm is based on Haar wavelet collocation technique (HWCT). Under certain conditions, we…
View article: Daily variation in sleep characteristics in individuals with and without post traumatic stress disorder
Daily variation in sleep characteristics in individuals with and without post traumatic stress disorder Open
Background Sleep disturbances are common in individuals with post traumatic stress disorder (PTSD). However, little is known about how daily variation in sleep characteristics is related to PTSD. This study examined the night-to-night and …
View article: Characterization of Sleep Disordered Breathing in Children with Duchenne Muscular Dystrophy Using AASM Criteria versus Disease Specific Criteria: What Is the Difference?
Characterization of Sleep Disordered Breathing in Children with Duchenne Muscular Dystrophy Using AASM Criteria versus Disease Specific Criteria: What Is the Difference? Open
RATIONALE:Duchenne muscular dystrophy (DMD) is the most common pediatric neuromuscular disorder.These individuals are at risk of developing sleep disordered breathing (SDB) and pulmonary exacerbations because of progressive muscle weakness…
View article: Haar wavelet method for solution of distributed order time-fractional differential equations
Haar wavelet method for solution of distributed order time-fractional differential equations Open
This manuscript is related to compute approximate solutions for a class of fractional distributed order differential equations (FDODEs). The corresponding derivative of fractional order is taken in Caputo sense. The adopted numerical schem…
View article: Numerical solution of the second order linear and nonlinear integro-differential equations using Haar wavelet method
Numerical solution of the second order linear and nonlinear integro-differential equations using Haar wavelet method Open
In this paper, a numerical algorithm is developed for the solution of second order linear and nonlinear integro-differential equations. The Haar collocation technique is applied to second order linear and nonlinear integro-differential equ…