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This study focuses on investigating the numerical solution of second-kind nonlinear Volterra–Fredholm–Hammerstein integral equations (NVFHIEs) by discretization technique. The purpose of this paper is to develop an efficient and accurate method for solving NVFHIEs, which are crucial for modeling systems with memory and cumulative effects, integrating past and present influences with nonlinear interactions. They are widely applied in control theory, population dynamics and physics. These equations are essential for solving complex real-world problems.

Demonstrating the solution’s existence and uniqueness in the equation is accomplished by using the Picard iterative method as a key technique. Using the trapezoidal discretization method is the chosen approach for numerically approximating the solution, yielding a nonlinear system of algebraic equations. The trapezoidal method (TM) exhibits quadratic convergence to the solution, supported by the application of a discrete Grönwall inequality. A novel Grönwall inequality is introduced to demonstrate the convergence of the considered method. This approach enables a detailed analysis of the equation’s behavior and facilitates the development of a robust solution method.

The numerical results conclusively show that the proposed method is highly efficacious in solving NVFHIEs, significantly reducing computational effort. Numerical examples and comparisons underscore the method’s practicality, effectiveness and reliability, confirming its outstanding performance compared to the referenced method.

Unlike existing approaches that rely on a combination of methods to tackle different aspects of the complex problems, especially nonlinear integral equations, the current approach presents a significant single-method solution, providing a comprehensive approach to solving the entire problem. Furthermore, the present work introduces the first numerical approaches for the considered integral equation, which has not been previously explored in the existing literature. To the best of the authors’ knowledge, the work is the first to address this equation, providing a foundational contribution for future research and applications. This innovative strategy not only simplifies the computational process but also offers a more comprehensive understanding of the problem’s dynamics.

This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized method (BiCGSTAB). The framework for the existence of the unique solutions of the integral equations is provided in the context of the Banach contraction principle and Bielecki norm.

The authors have applied the modified Lagrange polynomial method to approximate the numerical solutions of the second kind of weakly singular Volterra and Fredholm integral equations.

Approaching the interpolation of the unknown function using the aforementioned method generates an algebraic system of equations that is solved by an appropriate classical technique. Furthermore, some theorems concerning the convergence of the method and error estimation are proved. Some numerical examples are provided which attest to the application, effectiveness and reliability of the method. Compared to the Fredholm integral equations of weakly singular type, the current technique works better for the Volterra integral equations of weakly singular type. Furthermore, illustrative examples and comparisons are provided to show the approach’s validity and practicality, which demonstrates that the present method works well in contrast to the referenced method. The computations were performed by MATLAB software.

The convergence of these methods is dependent on the smoothness of the solution, it is challenging to find the solution and approximate it computationally in various applications modelled by integral equations of non-smooth kernels. Traditional analytical techniques, such as projection methods, do not work well in these cases since the produced linear system is unconditioned and hard to address. Also, proving the convergence and estimating error might be difficult. They are frequently also expensive to implement.

There is a great need for fast, user-friendly numerical techniques for these types of equations. In addition, polynomials are the most frequently used mathematical tools because of their ease of expression, quick computation on modern computers and simple to define. As a result, they made substantial contributions for many years to the theories and analysis like approximation and numerical, respectively.

This work presents a useful method for handling weakly singular integral equations without involving any process of change of variables to eliminate the singularity of the solution.

To the best of the authors’ knowledge, the authors claim the originality and effectiveness of their work, highlighting its successful application in addressing weakly singular Volterra and Fredholm integral equations for the first time. Importantly, the approach acknowledges and preserves the possible singularity of the solution, a novel aspect yet to be explored by researchers in the field.

This study aims to develop sweet chestnut incorporated corn-based extrudates by the optimization of process conditions.

The independent process variables for extrusion (blend ratio, barrel temperature, screw speed and feed moisture) were investigated to govern their impact on reliant variables, namely, bulk density, specific mechanical energy, water absorption index, water solubility index, color and hardness. Product and system responses were significantly (p < 0.05) affected by the independent variables. Experimental design with quadratic models experienced a high coefficient of determination (R² = 0.99).

Numerical optimization for the development of extrudates resulted in optimum conditions having corn flour: sweet chestnut flour (80:20), barrel temperature (120°C), screw speed (340 rpm) and feed moisture (12%). Fat, moisture and protein contents of the developed extrudates using optimum conditions were significantly (p < 0.05) lower compared to raw materials – corn and sweet chestnut. The packaging of extrudates in aluminum laminates revealed shelf stability of three months at room temperature without deterioration of quality.

Nutritionally rich sweet chestnut extruded products would be an exclusive option to already existing snacks in the market and can facilitate a new sphere in extruded product sector.

The purpose of the present study was to develop low Glycemic Index (GI) crackers from water chestnut flour (WCF) and barley flour (BF).

Five blends were prepared by mixing WCF with BF in the proportion of 100:0, 70:30, 50:50, 30:70 and 0:100, respectively. The baking process as well as ingredients were modified for the production of low GI crackers.

BF incorporation had significant (p < 0.05) effect on physical characteristics, organoleptic attributes and glycemic response of crackers. The resistant starch content of final product was found to be higher than WCF and BF. The research confirmed that replacement of 30 percent WCF with BF is feasible for development of low GI crackers with desired sensory attributes. The inference drawn from storage studies was that the developed crackers can be stored safely (with an overall acceptability score of greater than three on a 5-point scale) in metallized polyethylene up to 35 days under refrigerated conditions and 28 days under ambient conditions.

Although low GI crackers were developed successfully from WCF and BF in the present study. However, detailed storage studies of such crackers can be done in future so as to perform the tests of type-intensity and temporal dominance of sensation. Also, in view of their low GI, these crops need to be evaluated in future for development of other bakery products like bread, cake, muffins, etc.

Water chestnut and barley despite having good nutritional profile and low GI are still considered as underutilized crops. In the present study, these crops were explored for development of low GI crackers especially for people suffering from diabetes. The outcome of this study will open up a new window in the baking sector to develop low GI crackers viz-a-viz will add value to these crops which will help to provide remunerative returns to those who are directly or indirectly involved in trade of these underutilized crops.

This was the first reported innovative attempt to develop low GI crackers from WCF and BF. For development of crackers having desired sensory characteristics, it was found feasible to blend WCF and BF in the ratio of 70:30.

The present study aims to examine the moderating impact of governance quality on the tourism poverty nexus using a panel of six South Asian Association for Regional Cooperation (SAARC) countries during the period 2002 to 2019.

For the soundness of the results, fully modified ordinary least square (FMOLS) and dynamic ordinary least square (DOLS) econometric models were applied to determine the long-run relationship.

The findings confirmed the positive and significant impact of tourism development (international tourism arrival) and governance quality (effectiveness of governmental services) on poverty (per capita household consumption) reduction. Interestingly results confirm that governance quality and tourism development have complementary impacts on poverty reduction.

The present study has twofold contributions; First, despite the high potential of SAARC tourism, research remains limited in studies examining the role of tourism and governance quality on poverty reduction within the SAARC region. As a result, the present paper presents critical insights into the impact of tourism inflow and governance quality on poverty reduction in South Asian countries. Second, to the best of the author's knowledge, this is the first attempt to conduct an econometric analysis to examine the role of governance quality on the relationship between tourism inflow and poverty reduction in SAARC countries.

The purpose of this study is to investigate whether Tawarruq Islamic home financing (IHF) products remain untouched and maintain their position as the top IHF product in Malaysia.

The study adopted a qualitative research methodology that included both literature review and content analysis. Firstly, the existing studies and literature were reviewed to compare different types of IHF. The composition of IHF products offered by these Islamic banks was then investigated further to analyse each bank’s progress in IHF from 2015 to 2019. The data were gathered from bank websites, brochures, product disclosure sheets and annual reports.

The findings reveal that around 62.5% of Islamic banks offered Tawarruq for IHF in the year 2020. For the banks that offered Tawarruq, the amount of the financing continued to grow each year. The plausible reason for the preference for Tawarruq was its less risky nature, despite facing numerous operating, legal and Shariah issues.

This study has several limitations, including the fact that it was limited to home financing products only, the methodology used and the research period.

This study aimed to provide beneficial insights into the use of Tawarruq, which has been a source of concern for regulators as well as steps made to reduce its usage in the industry. Islamic banks should be more proactive in developing non-Tawarruq products to enhance product innovation in the market and minimise the heavy reliance on debt-based products.

This study provides useful insights by analysing IHF in depth for each Islamic bank and making recommendations for future research. Specifically, the method facilitated critical discussions and comparisons to previous research findings as to why Tawarruq has remained popular.

The purpose of the study is to measure the performance level of halal compliance practices by the halal-certified restaurants in Malaysia and rank and rate them based on several dimensions of halal compliance.

A total of 320 halal restaurants were surveyed. The absolute measurement approach of the analytic hierarchy process (AHP) was applied to rank and rate the restaurants. Finally, ANOVA and independent t-test were applied to assess if there is any significant difference in halal compliance performance between different groups of the respondents.

The AHP application resulted in only 19 restaurants (5.94%) achieving an “Excellent” rating. A significant difference has been observed between different groups of the respondents regarding their halal compliance performance.

An onsite audit and ranking of all the restaurants in Malaysia were beyond the scope of the study. The research was able to rank only 320 restaurants across Malaysia.

The findings and methodology of the study will provide policymakers with a clear roadmap for establishing a comprehensive rating system in the fields of the halal food industry to enhance the quality and integrity of the halal food management system.

To the best of the authors’ knowledge, this is the first time an empirical approach, like AHP, has been used to determine how Malaysia’s halal-certified restaurants stack up against one another. Similar studies can be carried out in other sectors of the halal industry as well as in similar context.

The purpose of this paper is to contribute to the existing body of work in the area of Islamic microfinance by examining the co‐operative nature of Islamic financial services providers (IFSPs) in Australia.

The method employed in this study is a mixture of one of the authors' post‐graduate research and their personal experience, curiosity and association with this industry.

Islamic financial cooperatives, relevant government authorities and Islamic micro‐lenders in Australia should cautiously examine the following opportunities for the development of Islamic microfinance in Australia: merging of Islamic cooperatives with each other for their future growth and development through attracting more capital; integration of microfinancing Islamic investment and retail banking facilities to provide the twin engines of fulfilling communities' religious needs and Australia's economic development; and introducing more creative Islamic microfinance techniques to suit the financial needs of individuals and groups to facilitate their contribution in the country's economic development.

The paper offers: an introduction to the emergence and development of Islamic microfinance in Australia; studies the current realities of the Islamic financial system of Australia from the perspective of Islamic microfinance contracting perspectives; explains the key role of IFSPs in Australia in fulfilling the microfinance needs of Muslim community; and examines the Islamic microfinance techniques they use.

Examination of the issues of the study is undertaken aiming at introducing Islamic microfinance with relevant parties including government authorities and Islamic micro‐lenders in Australia to find it as a viable alternative system of financing for Muslims in Australia.

The current study investigates the role of consumer ethnocentrism (CE) in the context of locally produced organic food. This research work further extends the extended theory of planned behavior (TPB) model by examining the mediating effect of extended TPB variables (ATT, SN, PBC, PV) between CE and PI for locally produced organic food.

Data were obtained from the visitors of two shopping malls situated in a large, heavily populated city of India using survey method. Further, two-step approach was applied to analyze the hypothesized model.

Findings indicate that CE is a substantial determinant of PI for locally produced organic food. Moreover, extended TPB mediates the relation between CE and PI for locally produced organic food.

Post Covid-19, market size of organic food is rapidly growing in India. In this regard, this study presents useful implications for the marketers of organic food for gaining better consumer insights to further develop appropriate marketing strategies.

CE has been found to be a useful predictor of their food attitudes. However, studies, investigating the role of CE in the context of sustainable food consumption, are scant. Moreover, studies exploring the mediating effect of extended TPB variables are also very limited.

The literature about the dynamics of Muslims' awareness and perception of waqf has been generally scarce,especially in Nigeria. As renewed efforts are emerging to develop a new waqf regime in the country, this study examines this aspect in Gombe metropolis, Nigeria, with a view to identifying the key factors shaping people's perception and awareness towards waqf.

To achieve the objective of this study, primary data were collected through a survey among 494 business owners in the Gombe metropolis. The data were then analysed using probit and Tobit regression models.

The study found that altruistic behaviour, religiosity level, educational level and young age are among the factors that determine people's perception and awareness towards donating to waqf among business owners in Gombe. Altruism and young age embolden businesspersons to recognise the effectiveness of waqf institutions in solving socioeconomic challenges.

The findings of this study imply that waqf has huge potential in the study area and that with well-structured, organized waqf education programmes within the business community using diverse avenues, a robust waqf sector can be developed.

As far as the study area and the entire Nigerian Islamic economics and finance landscape is concerned, the study has explored a novel research area. Given the infant stage of empirical studies on waqf in Nigeria, there are virtually no previous attempts to examine the awareness and perception of businesspersons towards waqf; variables that are key to the development of an effective sector.