Abstract
This paper deals with the existence of solutions for a new boundary value problem involving mixed generalized fractional derivatives of Riemann-Liouville and Caputo supplemented with nonlocal multipoint boundary conditions. The existence results for inclusion case are also discussed. The nonlinear term belongs to a general abstract space, and our results rely on modern theorems of fixed point. Ulam stability is also presented. We provide some examples that well-illustrate our main results.
Highlights
Introduction and PreliminariesIn this paper, we study a new generalized boundary value problem (GBVP) that involves both generalized RiemannLiouville and Caputo derivatives via nonlocal multipoint and generalized fractional integral boundary conditions given by 8 >>>>>>>>>< RL Dα0+,ρC Dβ0+ yðt Þ, m yð0Þ = α1 〠 σi I q,ρ 0+
We study a new generalized boundary value problem (GBVP) that involves both generalized RiemannLiouville and Caputo derivatives via nonlocal multipoint and generalized fractional integral boundary conditions given by
Jarad et al [3] proposed a new generalized fractional calculus based on a special case of proportional derivatives where the kernel of the fractional operator involves an exponential function
Summary
We study a new generalized boundary value problem (GBVP) that involves both generalized RiemannLiouville and Caputo derivatives via nonlocal multipoint and generalized fractional integral boundary conditions given by 8 >>>>>>>>>
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