Cauchy Problem for Fractional Order Second Type Volterra Equation

Year 2020, Volume: 3 Issue: 2, 33 - 39, 30.12.2020

Gülizar Alisoy , Gözde Arslantaş

Abstract

The presence of different definitions of derivatives in the mathematical analysis of fractional order allows you to get the best solution in accordance with the definition of various scientific and technical problems. Therefore, interest in the use of fractional-order differential equations in problems of mathematical modeling is progressively increasing. In this study, in the continuous and integrable space of functions B_(p,θ)^() (G,s) -Dzhabrailov-Alisoy, we study a Cauchy-type problem for D_a^ν y(x)=f[x,y(x)]-differential equations of fractional order on a G⊂R

Keywords

Fractional order differential equation, Riemann-Liouville derivative and integral, Cauchy problem, Dzhabrailov-Alisoy functions space

Kesirli Mertebe İkinci Çeşit Volterra Denklemi İçin Cauchy Problemi

Abstract

Kesirli mertebe matematik analizde farklı türev tanımlarının varlığı, değişik fen ve mühendislik problemlerinin tanımlanma biçimine uygun olarak en iyi çözümünün elde edilmesine olanak sağlamaktadır. Bu nedenle, matematiksel modelleme problemlerinde kesirli mertebe diferintegral denklemlerin kullanımına olan ilgi giderek artmaktadır. Bu çalışmada, sürekli ve integrallenebilir fonksiyonların B_(p,θ)^()(G,s)-Dzhabrailov-Alisoy uzayında, G⊂R olmak üzere, D_a^ν y(x)=f[x,y(x)]- kesirli mertebeden diferansiyel denklemler için bir Cauchy tipi problem incelenmiştir.

Keywords

Cauchy problemi, Dzhabrailov-Alisoy fonksiyonlar uzayı, Kesirli mertebe diferansiyel denklem, Riemann-Liouville türev ve integrali

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