Existence and stability of Hadamard p-type fractional functional differential equations

Abstract

Abstract:In this paper, we investigate initial value problems for Hadamard p-type fractional order functional and neutral functional differential equations. Sufficient conditions which guarantee the existence and Hyers-Ulam stability are new and obtained by some classical fixed point theory. Examples are also given to illustrate our theoretical results.

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].…”

“…In [32], the authors used Banach and Schauder fixed point theorem to obtain the existence and Hyers-Ulam stability of solutions for Hadamard fractional impulsive Cauchy problems of the form…”

Positive solutions for a class of nonlinear Hadamard fractional differential equations with a parameter

“…On the other hand, fractional differential equations can better describe many phenomena than ordinary differential equations in many diverse and widespread fields of science and engineering. For the development of fractional calculus and applications, we refer the reader to [1][2][3][4][5][6][7][8][9][10] and the references therein. For example, by employing the Avery-Henderson fixed-point theorem, Li [11] obtained the existence of positive solutions as considered for a fractional differential equation with p-Laplacian operator.…”