Integro-Differential Boundary Conditions to the Sequential ψ 1 -Hilfer and ψ 2 -Caputo Fractional Differential Equations

Surang Sitho, Sotiris K. Ntouyas, Chayapat Sudprasert and Jessada Tariboon ()
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Surang Sitho: Department of Social and Applied Science, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Chayapat Sudprasert: Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Jessada Tariboon: Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

Mathematics, 2023, vol. 11, issue 4, 1-12

Abstract: In this paper, we introduce and study a new class of boundary value problems, consisting of a mixed-type ψ 1 -Hilfer and ψ 2 -Caputo fractional order differential equation supplemented with integro-differential nonlocal boundary conditions. The uniqueness of solutions is achieved via the Banach contraction principle, while the existence of results is established by using the Leray–Schauder nonlinear alternative. Numerical examples are constructed illustrating the obtained results.

Keywords: ? -Hilfer fractional derivative; Caputo fractional derivative; boundary value problems; nonlocal boundary conditions; existence; uniqueness; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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