Here we do not consider the fD of the sumeax+e−ax.Letb, c, r, ψ∈R>0,x∈R,andletb±ic=re±iψ.ThenwehaveWDν0e−(b±ic)x=rνe−bx∓i(cx−νψ),LDν−πe(b±ic)x=rνebx±i(cx+νψ),WDν0(e−bxcoscx)=rνe−bxcos(cx−νψ),LDν−π(ebx...
We study the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations subject to multi-point boundary conditions which contain fractional derivatives.
$$ c_{1}=\frac{1}{\Lambda} \Biggl(\int _{0}^{\infty}h(s)\,ds-\sum_{i=1}^{m-2} \beta _{i}I^{\gamma_{i},\delta_{i}}_{\eta_{i}}I^{\alpha}h( \xi_{i}) \Biggr), $$ (2.8) where Λ is defined by (2.2). Thus, the unique solution of fractional boundary...
This article is a study on the (k,s)-Riemann–Liouville fractional integral, a generalization of the Riemann–Liouville fractional integral. Firstly, we introduce several properties of the extended integral of continuous functions. Furthermore, we make t
On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions. Appl. Math. Comput. 2015, 266, 235–243. [Google Scholar] [CrossRef] Mei, Z.D.; Peng, J.G.; Gao, J.H. Existence and uniqueness of solutions for nonlinear general fractional ...