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Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

Computer Modeling in Engineering & Sciences 2024年第8期140卷 1619-1645页

作者： Nasser Sweilam Seham Al-Mekhlafi Aya Ahmed ahoud alsher. Emad Abo-Eldahab Mathematics Department Faculty of ScienceCairo UniversityGiza12613Egypt Mathematics Department Faculty of EducationSana’a UniversitySana’a1247Yemen Mathematics Department Faculty of ScienceHelwan UniversityCairo11795Egypt Department of Mathematics College of ScienceUniversity of BishaAl Namas67398-5644Saudi Arabia

In this paper,two crossover hybrid variable-order derivatives of the cancer model are ***ünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional *** existence,uniqueness,and stability of the proposed model are *** Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed *** studies with generalized fifth-order Runge-Kutta method are *** examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are *** have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

关键词： Cancer diseases hybrid variable-order fractional derivatives adams bashfourth fifth step generalized fifth order Runge-Kutta method

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Spinal dural arteriovenous fistula:a comprehensive review of the history,classification systems,management,and prognosis

引用

Chinese Neurosurgical Journal 2024年第1期10卷 48-56页

作者： Ali Alkhaibary ahoud Alharbi Nada Alnefaie Hajar Alammar Alshaymaa M.Arishy Noor Alghanim Yazeed M.Aldhfyan Arwa Albaiahy Yahya H.Khormi Wael Alshaya Saad AlQahatani Ahmed Aloraidi Ahmed Alkhani Sami Khairy College of Medicine King Saud Bin Abdulaziz University for Health SciencesRiyadhSaudi Arabia King Abdullah International Medical Research Center RiyadhSaudi Arabia Division of Neurosurgery Department of SurgeryKing Abdulaziz Medical CityMinistry of National Guard-Health AffairsRiyadhSaudi Arabia Department of Neurosurgery National Neurosciences InstituteKing Fahad Medical CityRiyadhSaudi Arabia College of Medicine Jazan UniversityJazanSaudi Arabia Department of Neurosurgery King Faisal Specialist Hospital and Research CenterRiyadhSaudi Arabia Department of Surgery Faculty of MedicineJazan UniversityJazanSaudi Arabia

Spinal dural arteriovenous fistulas account for the majority of spinal vascular *** are typically located in the thoracolumbar region and are diagnosed in the middle-aged and elderly *** spinal dural arteriovenous fistulas have been postulated to be acquired,their exact development remains ***,the arteriovenous shunt is situated close to the spinal nerve root,inside the dura mater,where the blood from the radiculomeningeal artery and radicular vein *** history,there have been multiple classification systems of spinal arteriovenous shunts since *** were mainly based on the evolution of diagnostic studies as well as the treatment of these *** classification systems have undergone significant changes over the *** intracranial dural arteriovenous fistula,spinal dural arteriovenous fistula is progressive in *** neurological manifestations,due to venous congestion,tend to be insidious as well as *** include sensory deficits,such as paresthesia,bilateral and/or unilateral radicular pain affecting the lower limbs,and gait *** dural arteriovenous fistulas can be suspected on magnetic resonance imaging/magnetic resonance angiography and confirmed by digital subtraction angiography(DSA).The management includes surgery,endovascular therapy,and in selected cases,*** treatment goal of spinal dural arteriovenous fistula is to halt the progression of the *** prognosis depends on both the duration of symptoms as well as the clinical condition prior to *** present article comprehensively reviews the pathophysiology,changes in classification systems,natural history,clinical manifestations,radiological features,management,and prognosis.

关键词： Connection Endovascular Myelopathy Vascular

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