Fahad M. Alotaibi

In this paper, a class of integrodifferential equations with the Caputo fractal-fractional derivative is considered. We study the exact and numerical solutions of the said problem with a fractal-fractional differential operator. The abovementioned operator is arising widely in the mathematical modeling of various physical and biological problems. In our scheme, first, the integrodifferential equation with the fractal-fractional differential operator is converted to an integrodifferential equation with the Riemann–Liouville differential operator. Additionally, the obtained integrodifferential equation is then converted to the equivalent integrodifferential equation involving the Caputo differential operator. Then, we convert the integrodifferential equation under the Caputo differential operator using the Laplace transform to an algebraic equation in the Laplace space. Finally, we convert the obtained solution from the Laplace space into the real domain. Moreover, we utilize two techniques which include analytic inversion and numerical inversion. For numerical inversion of the Laplace transforms, we have to evaluate five methods. Extensive results are presented. Furthermore, for numerical illustration of the abovementioned methods, we consider three problems to demonstrate our results.

Information security policy (ISP) plays a crucial role in maintaining the availability, confidentiality, and integrity of sensitive data. However, it is of high complexity and heterogeneity due to the variety and redundancy of security policy practices and complexity of organisational systems. Various and duplicate ISP models and frameworks have been offered in the literature. The duplicate security policy practices, procedures, and processes in the existing models have made ISP disorganised, unstructured, and unclear to organisational users. As a result, there is still a need for a standardised and integrated model to make it simpler to share, manage, and reuse ISP practices amongst the organisations. The main objective of this study is to construct a metamodel to unify, organise, and structure ISP practices. By identifying, recognising, extracting, and combining the common information security policy practices from various ISP models in a built ISP metamodel called ISPM, we seek to make it simple for users and field specialists to derive/instantiate security policy models for their organisations. The development and validation process of the ISPM is based on the common security frameworks such as ISO 27001 frameworks. The developed ISPM consists of 19 common security practices: organisation, risk management, access control policy, edit, review, compliance, business management, backup and recovery, incident response, SETA program, security awareness, security training, security education, email security policy, cloud security policy, network security policy, website security policy, physical security policy, and privacy security policy. Each common security practice consists of several operations and attributes. The performance of the developed ISPM was compared to that of other models to evaluate its completeness and logicalness. Using ISO 27001 as a framework, the findings confirmed the comprehensiveness of ISPM. Therefore, it can contribute to organisations’ security by helping them to develop their own security policy models.

The fractional diffusion equation is one of the important recent models that can efficiently characterize various complex diffusion processes, such as in inhomogeneous or heterogeneous media or in porous media. This article provides a method for the numerical simulation of time-fractional diffusion equations. The proposed scheme combines the local meshless method based on a radial basis function (RBF) with Laplace transform. This scheme first implements the Laplace transform to reduce the given problem to a time-independent inhomogeneous problem in the Laplace domain, and then the RBF-based local meshless method is utilized to obtain the solution of the reduced problem in the Laplace domain. Finally, Stehfest’s method is utilized to convert the solution from the Laplace domain into the real domain. The proposed method uses Laplace transform to handle the fractional order derivative, which avoids the computation of a convolution integral in a fractional order derivative and overcomes the effect of time-stepping on stability and accuracy. The method is tested using four numerical examples. All the results demonstrate that the proposed method is easy to implement, accurate, efficient and has low computational costs.