Existence of solutions by fixed point theorem of general delay fractional differential equation with $ p $-Laplacian operator

Abstract

<abstract><p>In this manuscript, the main objective is to analyze the existence, uniqueness,(EU) and stability of positive solution for a general class of non-linear fractional differential equation (FDE) with fractional differential and fractional integral boundary conditions utilizing $ \phi_p $-Laplacian operator. To continue, we will apply Green's function to determine the suggested FDE's equivalent integral form. The Guo-Krasnosel'skii fixed point theorem and the properties of the $ p $-Laplacian operator are utilized to derive the existence results. Hyers-Ulam (HU) stability is additionally evaluated. Further, an application is presented to validate the effectiveness of the result.</p></abstract>

On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

“…The classical Banach contraction theorem [1] is an important and fruitful tool in nonlinear analysis. In the past few decades, many authors have extended and generalized the Banach contraction mapping principle in several ways (see [2][3][4][5][6][7][8][9][10][11][12]). On the other hand, several authors, such as Boyd and Wong [13], Browder [14], Wardowski [15], Jleli and Samet [16], and many other researchers have extended the Banach contraction principle by employing different types of control functions (see [17][18][19][20][21] and the references therein).…”