SOME NOVEL RESULTS ON THE EXISTENCE AND UNIQUENESS OF A POSITIVE SOLUTION TO A KIND OF NONLINEAR FRACTIONAL BOUNDARY VALUE PROBLEMS

Ahmadkhanlu, Asghar; Ertürk, Vedat; Kumar, Pushpendra

doi:10.46793/kgjmat2604.613a

SOME NOVEL RESULTS ON THE EXISTENCE AND UNIQUENESS OF A POSITIVE SOLUTION TO A KIND OF NONLINEAR FRACTIONAL BOUNDARY VALUE PROBLEMS

Ahmadkhanlu A., Ertürk V. S., Kumar P.

Kragujevac Journal of Mathematics, cilt.50, sa.4, ss.613-631, 2026 (ESCI, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 50 Sayı: 4
Basım Tarihi: 2026
Doi Numarası: 10.46793/kgjmat2604.613a
Dergi Adı: Kragujevac Journal of Mathematics
Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
Sayfa Sayıları: ss.613-631
Anahtar Kelimeler: fixed point theorem, Fractional boundary value problem, Green’s function, Riemann-Liouville derivative and integral
Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

This work investigates a fractional boundary value problem in the sense of Riemann-Liouville derivative and integral. We derive some novel results for the necessary and sufficient conditions for the existence and uniqueness of the positive solution. In this regard, some fixed-point theorems on cones are used. Also, a convergent successive sequence to find the solution to the problem is introduced. We derive the numerical scheme for the proposed problems. The correctness of the proposed results is verified with some illustrative examples.