Study on the integro-differential equations on \(C^1(\mathbb{R}_+)\). (English) Zbl 07658818
Summary: This paper provides sufficient conditions for the existence of a solution for some classes of integro-differential equations in unbounded domains. The investigation successfully applies the Darbo fixed point theorem by considering an appropriate measure of noncompactness on \(C^1(\mathbb{R}_+)\). Moreover, the paper contains some examples to illustrate the results in each type of the considered integro-differential equations. Further, some significant examples are solved by a numerical approach named the artificial small parameter method.
MSC:
| 47N20 | Applications of operator theory to differential and integral equations |
| 45J05 | Integro-ordinary differential equations |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
| 47H10 | Fixed-point theorems |
Keywords:
fixed-point theorems; integro-ordinary differential equations; measures of noncompactness; condensing mappingsReferences:
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