A study of a coupled system of Hadamard fractional differential equations with nonlocal coupled initial-multipoint conditions

Abstract

In this paper, we obtain the existence results for a coupled system of Hadamard fractional differential equations supplemented with nonlocal coupled initial-multipoint conditions via fixed point theorems. An example is constructed for the illustration of the uniqueness result.

On solvability of the non-local problem for the fractional mixed-type equation with Bessel operator

“…Further, after substituting ( 14) and ( 15) into the eq. ( 6) and initial conditions ( 16), ( 17), (18), we obtain the following prdoblems…”

“…We notice that while have been investigated the initial-boundary value or non-local problems involving popular class of differential operators like Riemann-Liouville, Caputo [16], [17], Hilfer fractional derivatives, Hadamard [18], Hilfer-Hadamard, Prabhakar, Atangana-Baleanu [19] the interest to another type of the differential operators is increased by many scientists, for instance, the hyper-Bessel differential operator [20], [21] is becoming main target of research. The importance of the hyper-Bessel differential operator is increasing since introduced by Dimovski [22] because of its applications in science.…”

Existence of Positive Solutions for a Coupled System of p-Laplacian Semipositone Hadmard Fractional BVP

“…As is wellknown, Hadamard's renowned fractional derivative from 1892 is the Hadamard fractional derivative [29]. To the author's knowledge, there have not been many works on this topic in previous decades; however, there have been more investigations into Hadamard FOBVP [30][31][32][33][34][35]. We address the presence of positive solutions to a linked system of Hadamard FOBVP in this study in light of the aforementioned factors as well as current developments in the field.…”

Deterministic and Stochastic Fractional-Order Hastings-Powell Food Chain Model

“…Thus, the stochastic models may be a more appropriate way of modeling the Hastings-Powell food chain model in many circumstances [17,18]. Recently, fractional calculus has been applied to describe different mathematical models, and it has been shown to be more accurate in some cases compared to the classical models [19][20][21][22][23][24][25][26]. The main objective of this paper is to study the deterministic and stochastic fractional-order Hastings-Powell model incorporating harvesting.…”