‎in this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{t}^{kappa^{2}}}:=j,;;1

Abstract The standard problem for the classical heat equation posed in a bounded domain $$\Omega $$ Ω of $${\mathbb {R}}^n$$ R n is initial and boundary value problem. If Laplace operator replaced by version fractional Laplacian, ...

The aim of this research work is to derive some appropriate results for extremal solutions a class generalized Caputo-type nonlinear fractional differential equations (FDEs) under boundary conditions (NBCs). aforesaid are derived by using the monotone iterative method, which exercises procedure upper and lower solutions. Two sequences generated in one converges other corresponding solution. met...

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...