TY - JOUR

T1 - Existence of solutions for a higher order Riemann–Liouville fractional differential equation by Mawhin's coincidence degree theory

AU - Domoshnitsky, Alexander

AU - Srivastava, Satyam Narayan

AU - Padhi, Seshadev

N1 - Publisher Copyright:
© 2023 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.

PY - 2023

Y1 - 2023

N2 - In this paper, we investigate the existence of at least one solution to the following higher order Riemann–Liouville fractional differential equation with Riemann–Stieltjes integral boundary condition at resonance: (Formula presented.) by using Mawhin's coincidence degree theory. Here, (Formula presented.) is the standard Riemann–Liouville fractional derivative of order (Formula presented.), and (Formula presented.) is the Riemann–Stieltjes integral of (Formula presented.) with respect to (Formula presented.). Our choice of (Formula presented.) in the boundary condition can be any integer between 0 and (Formula presented.), which supplements many boundary conditions assumed in the literature. Several examples are given to strengthen our result.

AB - In this paper, we investigate the existence of at least one solution to the following higher order Riemann–Liouville fractional differential equation with Riemann–Stieltjes integral boundary condition at resonance: (Formula presented.) by using Mawhin's coincidence degree theory. Here, (Formula presented.) is the standard Riemann–Liouville fractional derivative of order (Formula presented.), and (Formula presented.) is the Riemann–Stieltjes integral of (Formula presented.) with respect to (Formula presented.). Our choice of (Formula presented.) in the boundary condition can be any integer between 0 and (Formula presented.), which supplements many boundary conditions assumed in the literature. Several examples are given to strengthen our result.

KW - boundary value problems

KW - coincidence degree theory

KW - existence of solutions

KW - fractional derivatives and integrals

KW - Green's function

KW - Riemann–Liouville derivative

UR - http://www.scopus.com/inward/record.url?scp=85145403103&partnerID=8YFLogxK

U2 - 10.1002/mma.9005

DO - 10.1002/mma.9005

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AN - SCOPUS:85145403103

SN - 0170-4214

VL - 46

SP - 12018

EP - 12034

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 11

ER -