Article
Mathematics, Interdisciplinary Applications
Thanin Sitthiwirattham, Muhammad Arfan, Kamal Shah, Anwar Zeb, Salih Djilali, Saowaluck Chasreechai
Summary: This article proposed a scheme for computing a semi-analytical solution to a fuzzy fractional-order heat equation in two dimensions, utilizing Laplace transform and decomposition techniques to establish a series solution. Validation through three examples showed that the obtained solution approximated the approximate solution of the proposed equation.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Mati Ur Rahman, Ali Althobaiti, Muhammad Bilal Riaz, Fuad S. Al-Duais
Summary: This article explores a biological population model using a specific numerical method. The numerical simulations reveal a relationship between the population density and the fractional order, showing that a higher fractional order leads to a higher population density. The results demonstrate that the method is suitable and highly accurate in terms of computational cost.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Ola Ragb, Abdul-Majid Wazwaz, Mokhtar Mohamed, M. S. Matbuly, Mohamed Salah
Summary: This paper aims to find an efficient numerical solution for fractional order Cauchy reaction-diffusion equations (CRDEs) by exploring and applying differential quadrature based on different test functions. The governing system is discretized using novel techniques of differential quadrature method and the fractional operator of Caputo kind. The accuracy and reliability of the numerical algorithms are verified through comparison with exact and semi-exact solutions, and convergence analysis is conducted using absolute errors and L-infinity errors.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Manar A. Alqudah, Rehana Ashraf, Saima Rashid, Jagdev Singh, Zakia Hammouch, Thabet Abdeljawad
Summary: The research introduces a fuzzy hybrid approach merged with a homotopy perturbation transform method to solve fuzzy fractional Cauchy reaction-diffusion equations with fuzzy initial conditions. The simulation results demonstrate that the fuzzy SHPTM is a viable strategy for precisely and accurately analyzing the behavior of the proposed model.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Vladimir E. Fedorov, Marko Kostic, Tatyana A. Zakharova
Summary: The fractional powers of generators for analytic operator semigroups are used to prove the existence and uniqueness of a solution of the Cauchy problem to a first order semilinear equation in a Banach space. By constructing fractional powers A(?) for an operator A, we prove the local unique solvability of the Cauchy problem to a fractional order quasilinear equation with Gerasimov-Caputo fractional derivatives. Abstract results are applied to study an initial-boundary value problem for a time-fractional order nonlinear diffusion equation.
FRACTAL AND FRACTIONAL
(2023)
Article
Materials Science, Multidisciplinary
Asif Khan, Amir Ali, Shabir Ahmad, Sayed Saifullah, Kamsing Nonlaopon, Ali Akgul
Summary: In this article, the behaviour of the time fractional nonlinear Schrodinger equation under two different operators are investigated. Numerical and analytical solutions are obtained using the modified double Laplace transform. The error analysis shows that the system depends primarily on time, with small errors observed for small time values. The efficiency of the proposed scheme is verified with examples and further analyzed graphically and numerically.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Qasim Khan, Anthony Suen, Hassan Khan, Poom Kumam
Summary: This article presents an efficient analytical technique for solving fractional partial differential equations and their systems using three different operators. Generalized schemes for each targeted problem under the influence of each fractional derivative operator are derived. Numerical examples of non-homogeneous fractional Cauchy equation and three-dimensional Navier-Stokes equations are obtained using the iterative transform method. The results under different fractional derivative operators are found to be identical, and the 2D and 3D plots confirm the close connection between the exact and obtained results. Furthermore, the proposed method shows higher accuracy according to the table.
Article
Mathematics, Interdisciplinary Applications
Yu-Ming Chu, Nehad Ali Shah, Hijaz Ahmad, Jae Dong Chung, S. M. Khaled
Summary: The paper implemented the Homotopy perturbation transform method and New Iterative transform method to solve the time-fractional Cauchy reaction-diffusion equation, showing that the approach is easy to implement and accurate, making it useful for solving engineering science problems.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics, Interdisciplinary Applications
Vaijanath L. Chinchane, Asha B. Nale, Satish K. Panchal, Christophe Chesneau
Summary: This paper investigates weighted fractional integral inequalities using the Caputo-Fabrizio fractional integral operator with non-singular e(-)((1-delta/delta)(k-s)()), 0 < delta < 1, and presents new extensions of weighted fractional integral inequalities based on a family of n positive functions defined on [0, infinity).
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
M. H. Heydari, Z. Avazzadeh, A. Atangana
Summary: In this paper, a coupled system of nonlinear reaction-advection-diffusion equations is generalized to a variable-order fractional one using the Caputo-Fabrizio fractional derivative. A new formulation of the discrete Legendre polynomials, namely the orthonormal shifted discrete Legendre polynomials, is introduced to establish an appropriate method for the system. The devised method transforms the system into a system of algebraic equations using these polynomials and their operational matrices with the collocation technique, which is proven to be accurate through the analysis of two numerical examples.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ivan Area, Juan J. Nieto
Summary: In this paper, the Prabhakar fractional logistic differential equation is considered and other logistic differential equations are recovered using appropriate limit relations, with solutions represented in terms of a formal power series. Numerical approximations are implemented using truncated series.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Applied
Iqbal M. Batiha, Abeer A. Al-Nana, Ramzi B. Albadarneh, Adel Ouannas, Ahmad Al-Khasawneh, Shaher Momani
Summary: This paper investigates the role of fractional calculus in describing the dynamics of the COVID-19 pandemic in Saudi Arabia. By utilizing fractional-order differential operators and a modified SEIR model, the authors demonstrate that the proposed fractional-order models outperform the classical model in accurately describing real data and predicting the number of cases. The findings of this study provide valuable insights for decision makers in formulating effective plans and strategies to combat the pandemic.
Article
Materials Science, Multidisciplinary
Israr Ahmad, Thabet Abdeljawad, Ibrahim Mahariq, Kamal Shah, Nabil Mlaiki, Ghaus Ur Rahman
Summary: This article presents an approximate analytical solution to the fractional order Swift-Hohenberg equation using a novel iterative method called Laplace Adomian decomposition method (LADM). Through this method, nonlinear FSH equations with and without dispersive terms are studied and results are compared through plots for different fractional orders. The article also explores the problem under Caputo-Fabrizio fractional order derivative (CFFOD) and provides examples to demonstrate the results.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Haiyong Xu, Lihong Zhang, Guotao Wang
Summary: This paper investigates the existence of extremal solutions for a nonlinear boundary value problem involving the Caputo-Fabrizio-type fractional differential operator. By utilizing a new inequality and applying a monotone iterative technique with upper and lower solutions, the main result is obtained. The paper concludes with an illustrative example.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Jiabin Xu, Hassan Khan, Rasool Shah, A. A. Alderremy, Shaban Aly, Dumitru Baleanu
Summary: The research paper presents an efficient technique for solving fractional-order nonlinear Swift-Hohenberg equations related to fluid dynamics, showing that the Laplace Adomian decomposition method requires minimal calculations and produces solutions in close agreement with other existing methods. Numerical examples confirm the validity of the suggested method, demonstrating its almost identical solutions with various analytical methods through graphs and tables.
Article
Multidisciplinary Sciences
Meshari Alesemi
Summary: This study presents innovative methods for solving the time-fractional modified Degasperis-Procesi (mDP) and Camassa-Holm (mCH) models of solitary wave solutions. By combining the Elzaki transform (ET), homotopy perturbation method (HPM), and Adomian decomposition method (ADM), the proposed methods show improved accuracy in solving the models. Comparative analysis using numerical examples and plots demonstrate the effectiveness of the suggested techniques.
Article
Multidisciplinary Sciences
Meshari Alesemi
Summary: The suggested q-homotopy analysis transform method is applied to compute a numerical solution for a fractional parabolic equation with a fast convergent series. The effectiveness of the suggested technique is demonstrated through test examples and graphical results. The current method handles the series solution in a sizable admissible domain in an extreme way, providing a simple means of modifying the solution's convergence zone. The effectiveness and potential of the suggested algorithm are explicitly shown in the graphical results.
Article
Multidisciplinary Sciences
Meshari Alesemi, Jameelah S. Al Shahrani, Naveed Iqbal, Rasool Shah, Kamsing Nonlaopon
Summary: The exact solution to fractional-order partial differential equations is often difficult to obtain, so semi-analytical or numerical methods are commonly used. In this study, we combined the decomposition method with natural transformation to discover the solution to a system of fractional-order partial differential equations. The effectiveness of the proposed technique was demonstrated through specific examples, showing close correspondence between the exact and approximate solutions in graphical representation. We also examined the convergence of the proposed method with minimal calculations and its applicability to various fractional orders.
Article
Mathematics
Leila Ait Kaki, Nouria Arar, Mohammed S. Abdo, M. Daher Albalwi
Summary: In this paper, the mathematical analysis of time-dependent quasistatic processes involving contact between a solid body and a highly rigid structure (foundation) is considered. The constitutive law is assumed to be fractional long-memory viscoelastic. The contact problem is shown to be bilateral and modeled using Tresca's law. The existence of the generalized solution is established, supported by the surjectivity of the multivalued maximum monotone operator, Rothe's semidiscretization method, and arguments for evolutionary variational inequality.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Naveed Iqba
Summary: This paper investigates the mathematical result of the nonlinear fractional scheme of equations representing the singular and non-singular thermoelastic system. The suggested method, a combination of Shehu transformation with homotopy perturbation method and fractional derivative described with the Caputo operator, is proven to be effective through three evaluated cases of fractional-order models. The physical behavior of the fractional-order solution achieved is demonstrated through graphs, confirming the accuracy of the mathematical model. The suggested methodology is characterized as simple, organized, and accurate for studying nonlinear system differential equations of arbitrary order in engineering and science.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics
Meshari Alesemi
Summary: This research presents a combined approach utilizing an Elzaki transform, the homotopy perturbation method, and the Adomian decomposition method to solve nonlinear fractional shock wave equations. The nonlinear equation is transformed into an integral equation using the Elzaki transform, and then approximated using the homotopy perturbation method and Adomian decomposition method. The proposed method is evaluated through numerical experiments and compared with existing methods, demonstrating its accuracy and efficiency in solving nonlinear fractional shock wave equations.
Article
Mathematics
Mohammad Alshammari, Saleh Alshammari, Mohammed S. Abdo
Summary: This study explores two classes of hybrid boundary value problems involving psi-weighted Caputo-Fabrizio fractional derivatives and constructs the corresponding hybrid fractional integral equations based on the properties of the given operator. The existence theory for the given problems in the class of continuous functions is established and extended using Dhage's fixed point theory. Furthermore, analogous and comparable conclusions are offered as special cases, and two examples are provided as applications to illustrate and validate the results.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Hadeel Z. Alzumi, Hakima Bouhadjera, Mohammed S. Abdo
Summary: In this paper, we establish common fixed point results for expansive maps satisfying implicit relations in metric and dislocated metric spaces, by utilizing the concept of occasionally weakly biased maps of type A. These results refine previous studies on the theory of common fixed points. Several examples and a pertinent application are provided to demonstrate the viability and applicability of one of these results.
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES
(2023)
Article
Mathematics, Applied
H. Afshari, M. S. Abdo, M. N. Sahlan
Summary: This paper focuses on the boundary value problem for a fractional differential equation that involves a generalized Caputo fractional derivative in b spaces. The fractional operator used is specified by the kernel k(t; s) = psi(t) - psi(s) and the derivative operator 1/psi'(t) d/dt. Existence results are obtained using the fixed point theorem of alpha-phi-Graghty contraction type mapping. Finally, illustrative examples are provided to validate the obtained results.
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
(2023)
Article
Mathematics, Applied
Oussama Melkemi, Mohammed S. Abdo, Wafa Shammakh, Hadeel Z. Alzumi
Summary: The present article investigates the two-dimensional Euler-Boussinesq system with critical fractional dissipation and general source term. First, we show that this system admits a global solution of Yudovich type, and as a consequence, we treat the regular vortex patch issue.
Article
Engineering, Multidisciplinary
Lakhlifa Sadek, Otmane Sadek, Hamad Talibi Alaoui, Mohammed S. Abdo, Kamal Shah, Thabet Abdeljawad
Summary: In this study, a model is proposed to investigate the spread of COVID-19 using the fractional order Caputo derivative. The model considers different hospitalization strategies for severe and mild cases and incorporates an awareness program. The SEIR model is generalized to focus on the transmissibility of aware and ignorant individuals, as well as individuals with different symptoms. Numerical simulations and predictions are conducted, considering immunization and the effect of public awareness on transmission dynamics.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Naveed Iqbal, Muhammad Tajammal Chughtai, Roman Ullah
Summary: This article uses transformation and fractional Taylor's formula to find approximate solutions for non-linear fractional-order partial differential equations. The method is proved correct by solving non-linear Burgers' equations with correct starting data. A rapid convergence McLaurin series is used to obtain close series solutions for both models with less work and more accuracy. Three-dimensional figures are drawn to observe how time-Caputo fractional derivatives affect the results of the models, and the proposed method is found to be an easy, flexible, and helpful way to solve and understand a wide range of non-linear physical models.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Naveed Iqbal, Mohammad Alshammari, Wajaree Weera
Summary: In this study, the suggested residual power series transform method is used for computing the numerical solution of the fractional-order nonlinear Gardner and Cahn-Hilliard equations, resulting in a fast convergent series. The efficacy and leverage of this technique are demonstrated through test examples and the achieved results are proven graphically. The method presented offers a powerful handling of series solution in a sizable admissible domain and provides a simple means of modifying the solution's convergence zone, as explicitly shown in the graphical results.
Article
Mathematics, Applied
Ala Eddine Taier, Ranchao Wu, Naveed Iqbal
Summary: This paper studies a boundary value problem for a hybrid fractional integro-differential system involving the conformable fractional derivative. The existence and uniqueness of solutions are discussed using the Krasnoselskii fixed point theorem and the Banach fixed point theorem. An example is provided to illustrate the results.
Article
Engineering, Multidisciplinary
Muath Awadalla, Kinda Abuasbeh, Yves Yannick Yameni Noupoue, Mohammed S. Abdo
Summary: This study focuses on the dynamics of drug concentration in the blood and proposes a new modeling technique based on Caputo and Caputo-Fabrizio derivatives. The application of the technique on real data sets shows that the Caputo derivative is more suitable for this study.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
