The Exact Iterative Solution of Fractional Differential Equation with Nonlocal Boundary Value Conditions

Abstract

We deal with a singular nonlocal fractional differential equation with Riemann-Stieltjes integral conditions. The exact iterative solution is established under the iterative technique. The iterative sequences have been proved to converge uniformly to the exact solution, and estimation of the approximation error and the convergence rate have been derived. An example is also given to demonstrate the results.

The Unique Positive Solution for Singular Hadamard Fractional Boundary Value Problems

“…The way to attack this new problem follows a scheme similar to that used in [21], with the necessary adaptations that Hadamard fractional derivative contains logarithmic function of arbitrary exponent.…”

“…In the past ten years, fractional differential equations have been considered in many papers (see [11][12][13][14][15][16][17][18][19][20][21][22]). Most of the works on the topic have been based on Riemann-Liouville type and Caputo type fractional differential equations.…”

Uniqueness of Iterative Positive Solution to Nonlinear Fractional Differential Equations with Negatively Perturbed Term

“…In recent years, it has attracted the interest of many researchers and has become a hot-button issue [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Compared with the integer order, it has a wider range of applications as it can be used to describespecific problems more precisely, such as the problem in complex analysis, polymer rheology, physical chemistry, electrical networks, and many other branches of science, For specific applications, see [15,16,[20][21][22][23][24][25][26][27][28]. In [3], the authors study the following BVP:…”

Solutions for a Class of Hadamard Fractional Boundary Value Problems with Sign-Changing Nonlinearity

“…As is known, fractional differential equations have been paid special attention by many researchers for the reason that they serve as an excellent tool for wide applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, and control theory; for more details, we refer to books [1][2][3]. In recent years, there have been a large number of papers dealing with the existence of solutions of nonlinear initial (boundary) value problems of fractional differential equations by using some techniques of nonlinear analysis, such as fixed-point results [4][5][6][7][8][9][10][11][12][13], iterative methods [14][15][16][17][18][19][20][21][22][23], the topological degree [24][25][26][27][28][29], the Leray-Schauder alternative [30,31], and stability [32].…”