Exploring solutions to specific class of fractional differential equations of order \(3<\hat{u}\leq 4\). (English) Zbl 07896997
Summary: This paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order \(3<\hat{u} \leq 4\) and includes a term \(\Theta (\beta,\mathscr{Z}(\beta))\) alongside boundary conditions. Through the application of a fixed point theorem in appropriate function spaces, we consider nonlocal conditions along with necessary assumptions under which solutions to the given FDE exist. Furthermore, we offer an example to illustrate the results.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 47H10 | Fixed-point theorems |
Keywords:
fractional derivatives; differential equations; fractional differential equations; antiperiodic; nonlocal boundary conditions; existenceReferences:
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