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Higher order nonlocal nonlinear boundary value problems for fractional differential equations

Rahmat Ali Khan
대한수학회 (The Korean Mathematical Society)|2014.03|대한수학회보 (Bulletin of the KMS)|제51권 제2호|pp. 329-338

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키워드

upper and lower solutionsboundary value problemsfractional differential equationsthree-point boundary conditionsgeneralized quasilinearization
주제분류수학

초록

In this paper, we study the method of upper and lower so- lutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differ- ential equations of the type cDq 0+u(t) + f(t, u(t)) = 0, t ∈ (0, 1) u′(0) = u′(π), u′′(0) = 0, u′′′(0) = 0, . . . , u(n−1)(0) = 0, u(1) = u(π), where, n−1 < q < n, n(≥3) ∈ N, 0 < π,γ, δ < 1 and cDq 0+ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

Abstract

In this paper, we study the method of upper and lower so- lutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differ- ential equations of the type cDq 0+u(t) + f(t, u(t)) = 0, t ∈(0, 1) u′(0) = u′(π), u′′(0) = 0, u′′′(0) = 0, . . . , u(n−1)(0) = 0, u(1) = u(π), where, n−1 < q < n, n(≥ 3) ∈ N, 0 < π,γ,  <δ 1 and cDq 0+ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

참고문헌 (25)

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