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<p>This paper investigates a mixed fractional differential equation (FDE) involving both left-sided and right-sided Caputo fractional derivatives. Our primary contributions are as follows: First, we introduce foundational lemmas and definitions pertinent to the problem. Second, we develop a solution composed of Green’s function and an additional constant term, thoroughly determining the Green’s function and its properties. Third, we establish the existence of solutions using Krasnoselskii’s fixed point theorem and prove their uniqueness through the Banach fixed point theorem. These contributions collectively provide a robust framework for solving mixed FDEs, highlighting the utility of these mathematical methods in addressing complex fractional differential equations.</p>

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Analyzing the Existence and Uniqueness of Solutions in Coupled Fractional Differential Equations

  • 期刊论文

  • 发表日期：

    2025年3月16日

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  • Intesham Ansari,
  • Rishika Dubey,
  • Amita Devi,
  • Anoop Kumar

摘要

This paper investigates a mixed fractional differential equation (FDE) involving both left-sided and right-sided Caputo fractional derivatives. Our primary contributions are as follows: First, we introduce foundational lemmas and definitions pertinent to the problem. Second, we develop a solution composed of Green’s function and an additional constant term, thoroughly determining the Green’s function and its properties. Third, we establish the existence of solutions using Krasnoselskii’s fixed point theorem and prove their uniqueness through the Banach fixed point theorem. These contributions collectively provide a robust framework for solving mixed FDEs, highlighting the utility of these mathematical methods in addressing complex fractional differential equations.