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Existence of solutions for nonlinear fractional \(q\)-difference integral equations with two fractional orders and nonlocal four-point boundary conditions. (English) Zbl 1372.45007

Summary: We investigate the existence of solutions for a nonlinear fractional \(q\)-difference integral equation (\(q\)-variant of the Langevin equation) with two different fractional orders and nonlocal four-point boundary conditions. Our results are based on some classical fixed-point theorems. An illustrative example is also presented.

MSC:

45G10 Other nonlinear integral equations
47N20 Applications of operator theory to differential and integral equations
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