OJO, EZEKIEL KADEJO and Covenant University, Theses (2024) SOLVABILITY OF RESONANT FRACTIONAL ORDER BOUNDARY VALUE PROBLEMS WITH TWO-DIMENSIONAL KERNEL ON THE HALF-LINE. ["eprint_fieldopt_thesis_type_phd" not defined] thesis, Covenant University.
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Abstract
This research derives conditions for existence of solutions for resonant fractional order boundary value problems with multi-point and integral boundary conditions when the dimension of the kernel of the differential operator equals two on the half-line. Two classes of fractional order boundary value problems were investigated. The first class included two problems with linear differential operator of Riemann-Liouville type. Existence results were established by using Mawhin’s coincidence degree theory. The fractional order differential equations under consideration were transformed to abstract equation Lx(t) = Nx(t). The corresponding homogeneous equations were solved to establish conditions critical for resonance. For the first class of problems, it was shown that L is a Fredholm map of index zero and N is L−compact. The existence lemmas and theorem were stated and proved to establish that solutions exist for the two problems. The second class contained two p-Laplacian fractional order boundary value problems with nonlinear differential operator. Riemann-Liouville and Caputo type of fractional derivatives were involved. The extension of coincidence degree theory by Ge and Ren was applied to establish existence of solutions for the two problems. Conditions for resonance were derived by solving the corresponding homogeneous fractional p-Laplacian BVPs. The BVPs were transformed to abstract equations Mx(t) = Nλx(t), λ ∈ [0,1]. It was shown that M is a quasi-linear operator and Nλ is M−compact. The results obtained generalize and complement existing results in the literature, which are applicable in the sciences, engineering, finance and business. Examples were provided to substantiate the results obtained
| Item Type: | Thesis (["eprint_fieldopt_thesis_type_phd" not defined]) |
|---|---|
| Uncontrolled Keywords: | Keywords: Fractional order, half-line, integral boundary conditions, Mawhin’s coincidence degree, multi-point, p-Laplacian, resonance, two-dimensional kernel |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics |
| Depositing User: | nwokealisi |
| Date Deposited: | 19 Mar 2024 15:33 |
| Last Modified: | 19 Mar 2024 15:33 |
| URI: | http://eprints.covenantuniversity.edu.ng/id/eprint/17850 |
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