Influence of nonlocal discrete and integral boundary conditions involving Caputo derivative in boundary value problem

Analysis of boundary value problem with multi-point conditions involving Caputo-Hadamard fractional derivative

“…One of the main factors that represent the utility/prevalence of the subject is that fractional order derivatives and integrals are shown to be better devices for the representation of real components than integer orders. We refer the reader to the papers [6,8,11,18,19,20,21,22,23,26,27,4,30,3,17] for examples and information, and the references cited therein. A large part of the work on the subject was found to depend on Riemann-Liouville and Caputo FDEs.…”

Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives

“…The subject of the fractional boundary value problem (BVP) has been intensively discussed in recent years by several researchers and in the literature, for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references cited therein, where a variety of findings relevant to both the theoretical and implementation aspects of the topic can be found. It has improved the classic modeling of many significant materials and processes with the use of fractional calculus tools as a fractional-order operator can take the history of the phenomena involved into account.…”

Existence of Solutions for Nonlocal Boundary Value Problem of Hadamard Fractional Differential Equations

“…The monographs [14,15,16,18,20] have ordinarily referred to the hypothesis of fractional derivatives and integrals and applications to differential equations of fractional order. For more points of interest and models, see [1,4,5,6,9,10,17,24,25,26,27,28,29,21,22,23,31], and the references in that.…”