By proposing a new approach, we prove local existence and uniqueness of the solution when the nonlinear function on the right hand side of the equation under consideration is continuous on $(0,T]\times\mathbb{R}.$**********************************************************************************************************************************************************************************************************************************************************************************************
📌 3 Key Takeaways
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Objective & Hypothesis:In this article, we consider an initial value problem for a nonlinear differential equation with Riemann-Liouville fractional derivative.
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Key Findings & Data:In this article, we consider an initial value problem for a nonlinear differential equation with Riemann-Liouville fractional derivative.
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Conclusion & Impact:By proposing a new approach, we prove local existence and uniqueness of the solution when the nonlinear function on the right hand side of the equation under consideration is continuous on $(0,T]\times\mathbb{R}.$**********************************************************************************************************************************************************************************************************************************************************************************************
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional differential equations · mean value theorem · Nagumo-type uniqueness
Abstract
In this article, we consider an initial value problem for a nonlinear differential equation with Riemann-Liouville fractional derivative. By proposing a new approach, we prove local existence and uniqueness of the solution when the nonlinear function on the right hand side of the equation under consideration is continuous on $(0,T]\times\mathbb{R}.$**********************************************************************************************************************************************************************************************************************************************************************************************
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