Existence Result and Uniqueness for Some Fractional Problem

Abstract

In this article, by the use of the lower and upper solutions method, we prove the existence of a positive solution for a Riemann–Liouville fractional boundary value problem. Furthermore, the uniqueness of the positive solution is given. To demonstrate the serviceability of the main results, some examples are presented.

Caputo Proportional Fractional Differential Equation with Multi-point Boundary Condition

“…In [21,22], the authors studied the existence of solutions to boundary value problems involving fractional derivatives. Other similar works can be found in [23][24][25][26][27][28][29]31] Motivated and inspired by the aforementioned works, in this article, we consider the following proportional fractional differential equation with multi-point boundary condition of form:…”

Existence Results for a Class of Nonlinear Hadamard Fractional with p-Laplacian Operator Differential Equations

“…Some recent works on fractional differential equations involving Riemann Liouville and Caputo-type fractional derivatives are studied using nonlinear analysis methods such as Krasnoselskii fixed-point Theorems (Agarwal and O'Regan, 1998;Ghanmi and Horrigue, 2018;Guo et al, 2007;Guo et al, 2008), Leray-Schauder alternative (Ghanmi and Horrigue, 2019;Qi et al, 2017), sub-solution and super-solution methods (Wang et al, 2019;Mâagli et al, 2015) and iterative techniques (Liu et al, 2013). Hadamard (1892) introduced an important fractional derivative, which differs from the above-mentioned ones because its definition involves logarithmic function of arbitrary exponent and named as Hadamard derivative.…”

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

“…The main advantages of these operator is the freedom of choice of the function ψ and its merge and acquire the properties of the aforementioned fractional operators. Results based on these setting can be found in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The Ulam-Hyers stability point of view, is the vital and special type of stability that attracts many researchers in the field of mathematical analysis.…”