Triple positive solutions for nonlocal fractional differential equations with singularities both on time and space variables

Regional Enlarged Observability of Fractional Differential Equations with Riemann—Liouville Time Derivatives

“…Despite its development, the theory of fractional differential equations, compared with the classical theory of differential equations, is a field of research only on its initial stage of development, calling great interest to many mathematicians [28][29][30]. For distributed parameter systems, several works deal with the problem of regional observability, which we study here in the fractional context, investigating the possibility to reconstruct the initial state or gradient only on a subregion ω of the evolution domain Ω [31][32][33][34][35].…”

Positive solutions of semipositone singular fractional differential systems with a parameter and integral boundary conditions

“…The existence of solutions or positive solutions for such class of problems has attracted much attention (see [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] and the references therein).…”

Positive solutions for a class of fractional infinite-point boundary value problems

“…), FDE serve as an excellent instrument for the description of memory and hereditary properties of various materials and processes. During the last few decades, much attention has been paid to the study of boundary value problems (BVP for short) of fractional differential equation, such as the nonlocal BVP [1,3,7,13,18], singular BVP [6,8,11,19,20,25], semipositone BVP [14][15][16]23], resonant BVP [2,12], and impulsive BVP [10,27]. Since only positive solutions are meaningful in most practical problems, some work has been done to study the existence of positive solutions for fractional boundary value problems by using the techniques of nonlinear analysis.…”