Investigating Solutions of the Noyes-Whitney Dynamic Equation via Proportional Fractional Derivative

Öz

The dynamics of solid material dissolving in a solvent are fundamentally described by the Noyes-Whitney equation. For the purpose of simulating intricate processes with memory effects and non-local behaviors, fractional calculus offers a strong foundation. We explore the effects of memory and non-locality on dissolution kinetics by solving the Noyes-Whitney equation using fractional derivatives. By means of mathematical analysis, we provide insights into the dissolving processes in chemical engineering and pharmaceutical applications by clarifying the behavior of the Noyes-Whitney equation with proportional fractional derivative. In this study, after discussing the characteristics and theories of the proportional fractional derivative on a time scale, we solve the proportional fractional Noyes-Whitney dynamic equation in the presence of the initial condition and give several examples on various time scales via the proportional fractional derivative.

Anahtar Kelimeler

• Noyes-Whitney dynamic equation
• fractional calculus
• proportional fractional derivative

Noyes-Whitney Dinamik Denkleminin Çözümlerinin Oransal Kesirli Türeve Göre İncelenmesi

Öz

Katı maddenin bir çözücü içinde çözünmesinin dinamiği temel olarak Noyes-Whitney denklemi ile tanımlanır. Karmaşık süreçleri hafıza etkileri ve yerel olmayan davranışlarla simüle etmek amacıyla kesirli analiz güçlü bir temel sunar. Noyes-Whitney denklemini kesirli türevler kullanarak çözerek hafızanın ve yerel olmamanın çözünme kinetiği üzerindeki etkilerini araştırıyoruz. Matematiksel analiz yoluyla, Noyes-Whitney denkleminin orantılı kesirli türevle davranışını açıklığa kavuşturarak kimya mühendisliği ve farmasötik uygulamalardaki çözünme süreçlerine ilişkin bilgiler sağlıyoruz. Bu çalışmada oransal kesirli türevin özelliklerini ve teorilerini zaman ölçeğinde verdikten sonra oransal kesirli Noyes-Whitney dinamik denklemini başlangıç koşulunun varlığında ve oransal kesirli türev üzerinden çeşitli zaman ölçeklerinde birkaç örnek vererek çözüyoruz.

Anahtar Kelimeler

• Noyes-Whitney dinamik denklemi
• kesirli hesap
• oransal kesirli türev

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