Abstract
We discuss the existence of solutions for a Caputo type multi-term nonlinear fractional differential equation supplemented with generalized integral boundary conditions. The modern tools of functional analysis are applied to achieve the desired results. Examples are constructed for illustrating the obtained work. Some new results follow as spacial cases of the ones reported in this paper.
Highlights
Fractional calculus received overwhelming interest in view of its vast applications in the mathematical modeling of real world phenomena occurring in scientific and engineering disciplines
We introduce and study a nonlinear nonlocal-terminal value problem consisting of multiple Caputo fractional derivatives and generalized integral boundary conditions
The work presented in this paper is of quite general nature as the derived results specialize to the ones associated with Riemann–Liouville, Hadamard, Erdélyi-Kober and Katugampola type integral boundary conditions by fixing the parameters involved in generalized integral boundary conditions appropriately
Summary
Fractional calculus received overwhelming interest in view of its vast applications in the mathematical modeling of real world phenomena occurring in scientific and engineering disciplines. We introduce and study a nonlinear nonlocal-terminal value problem consisting of multiple Caputo fractional derivatives and generalized integral boundary conditions. N λi ρi Iθγii,,κδii y(ξi), η, ξi ∈ (0, T), i=1 where cDχ denotes the Caputo fractional derivatives of order χ ∈ {α, β, p} with 0 < χ < 1, p < β, ρi Iθγii,,κδii is the generalized fractional integral, γi > 0, δi, θi, κi, λi ∈ R, i = 1, 2, . The Riemann–Liouville fractional integral of a locally integrable real-valued function μ of order τ ∈ R (τ > 0) on −∞ ≤ a1 < t < a2 ≤ +∞, denoted by Jaτ is defined by t. The hypothesis of Krasnoselskii fixed point theorem [28] is satisfied, which leads to the conclusion that there exists at least one solution on [0, T]
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