Discrete Fractional-Order Modeling of Recurrent Childhood Diseases Using the Caputo Difference Operator by Yasir A. Madani, Zeeshan Ali, Mohammed Rabih, Amer Alsulami, Nidal H. E. Eljaneid, Khaled Aldwoah, Blgys Muflh

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Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator by Bushra Bajjah, Mahmut Modanli

“…Simulations are implemented via a finite difference method with Grünwald-Letnikov discretization approach for Caputo derivative operator to define how changes in parameters impact the dynamic behavior of the system using Matlab.…”
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Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization by Ibtissem Talbi, Adel Ouannas, Giuseppe Grassi, Amina-Aicha Khennaoui, Viet-Thanh Pham, Dumitru Baleanu

“…This paper provides a contribution to the topic by presenting a novel version of the fractional Grassi–Miller map, along with improved schemes for controlling and synchronizing its dynamics. By exploiting the Caputo h-difference operator, at first, the chaotic dynamics of the map are analyzed via bifurcation diagrams and phase plots. …”
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Applications of artificial intelligence for clusters analysis of Uranium decay via a fractional order discrete model by Hasib Khan, Jehad Alzabut, D.K. Almutairi

Subjects: “…Caputo’s difference operator…”
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Qualitative Analysis of a Hyperchaotic Lorenz-Stenflo Mathematical Model via the Caputo Fractional Operator by Chernet Tuge Deressa, Sina Etemad, Mohammed K. A. Kaabar, Shahram Rezapour

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A Comparative Study of Fractional-Order Diffusion Model within Atangana-Baleanu-Caputo Operator by Mohammad Alshammari, Naveed Iqbal, Davis Bundi Ntwiga

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Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense by Samson Olaniyi, Furaha M. Chuma, Sulaimon F. Abimbade

“…This result is significant for fighting and preventing Ebola epidemic in the population, since the Caputo derivative operator allows for effective description of the disease dynamics with memory, where the future evolution of the disease is governed by its prior history. …”
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The Z-Transform Method and Delta Type Fractional Difference Operators by Dorota Mozyrska, Małgorzata Wyrwas

“…The Caputo-, Riemann-Liouville-, and Grünwald-Letnikov-type difference initial value problems for linear fractional-order systems are discussed. …”
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Analysis of Fractional Differential Equations with the Help of Different Operators by Naveed Iqbal, Moteb Fheed Saad Al Harbi, Saleh Alshammari, Shamsullah Zaland

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Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications by Thabet Abdeljawad, Qasem M. Al-Mdallal, Mohamed A. Hajji

“…Recently, Abdeljawad and Baleanu have formulated and studied the discrete versions of the fractional operators of order 0<α≤1 with exponential kernels initiated by Caputo-Fabrizio. …”
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Analysis of Numerical Method for Diffusion Equation with Time-Fractional Caputo–Fabrizio Derivative by Hanxiao Wang, Xindong Zhang, Ziyang Luo, Juan Liu

“…In this paper, we propose a high-precision discrete scheme for the time-fractional diffusion equation (TFDE) with Caputo-Fabrizio type. First, a special discrete scheme of C-F derivative is used in time direction and a compact difference operator is used in space direction. …”
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Dynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factors by Saima Rashid, Abdul Bariq, Ilyas Ali, Sobia Sultana, Ayesha Siddiqa, Sayed K. Elagan

“…By taking into account the modified Atangana–Baleanu–Caputo (mABC) fractional difference operator, we develop an analytical framework for an outbreak caused by MPXV and broaden it to accommodate the fractional scenario. …”
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Analysis of school bullying menace incorporating family education: a mathematical modeling approach by Adejimi Adeniji, Adejimi Adeniji, Adejimi Adeniji, Emmanuel Addai, Shatalov Michael, Kekana Malesela, Joshua Kiddy K. Asamoah, Joshua Kiddy K. Asamoah, Kayode Oshinubi

“…An Adams-Bashforth method numerical scheme is presented, offering a robust approach for scenario simulations under the Caputo fractional operator. Scenario simulations shows the impact of family education on the prevalence and dynamics of school bullying. …”
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A Fractional-Order Investigation of Vaccinated SARS-CoV-2 Epidemic Model with Caputo Fractional Derivative by Badr Saad T. Alkahtani

“…In this paper, we consider a fractional-order mathematical system comprising four different compartments for the recent pandemic of SARS-CoV-2 with regard to global and singular kernels of Caputo fractional operator. …”
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Fractional-order boundary value problems solutions using advanced numerical technique by Asmat Batool, Imran Talib, Muhammad Bilal Riaz

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Multiparameter Fractional Difference Linear Control Systems by Dorota Mozyrska

“…The Riemann-Liouville-, Caputo-, and Grünwald-Letnikov-type fractional order difference operators are discussed and used to state and solve the controllability and observability problems of linear fractional order discrete-time control systems with multiorder and multistep. …”
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Spectral Collocation Method for Fractional Differential/Integral Equations with Generalized Fractional Operator by Qinwu Xu, Zhoushun Zheng

“…Generalized fractional operators are generalization of the Riemann-Liouville and Caputo fractional derivatives, which include Erdélyi-Kober and Hadamard operators as their special cases. …”
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Mathematical Modeling of Feelings in Viewpoint of Analysis of Olvido Poetry with Fractional Operators by Mustafa Ali Dokuyucu, Burak Armağan, Ülkü Eliuz, Ahmet Ocak Akdemir, Mehmet Emir Köksal

“…The solutions of this model are investigated with the help of Caputo and Atangana–Baleanu fractional derivative operators. …”
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A Fourth-Order Compact Finite Difference Scheme for Solving the Time Fractional Carbon Nanotubes Model by N. H. Sweilam, Khloud R. Khater, Zafer M. Asker, Waleed Abdel Kareem

“…The proportional Caputo hybrid operator has been used to fractionalize the proposed model. …”
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Solving class of mixed nonlinear multi-term fractional Volterra-Fredholm integro-differential equations by new development of HAM by Zainidin Eshkuvatov, Zaid Laadjal, Shahrina Ismail

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