Fractional Langevin equations with multi-point and non-local integral boundary conditions

A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions

“…It is worth remarkable to mention that the field of studying the existence and uniqueness of solutions to fractional differential equations has drawn attention of many contributors [21][22][23][24][25][26][27][28].…”

On the Existence and Uniqueness of Solution to Fractional-Order Langevin Equation

“…Unquestionably, the fractional calculus, which requires the order of the functional operator of calculus to be turned into the fractional case, is a forceful mathematical argument for providing much and more flexibility in dealing with many real-world applications [1,2]. More particularly, the fractional-order differential equations (FODEs), which are considered a cornerstone of this field, have been extensively employed in modeling several phenomena and numerous scientific applications such as diffusion modeling [3], robot manipulators [4], economics [5], and many more [6][7][8][9].…”

“…In particular, through using some special boundary conditions, some applicable results related to the existence of solutions for the FoLE have been reported in [28]. Both aspects have been investigated when the coupled incommensurate fractional-order systems were handled by Salem and Alnegga and Salem et al in [15,29]. However, in more recent times, numerous outcomes associated with those aspects have, moreover, been informed widely (see [1,14,21,[30][31][32][33][34]).…”

“…Both aspects have been investigated when the coupled incommensurate fractional-order systems were handled by Salem and Alnegga and Salem et al in [15,29]. However, in more recent times, numerous outcomes associated with those aspects have, moreover, been informed widely (see [1,14,21,[30][31][32][33][34]). In more concrete terms, some useful theoretical tools, like the so-called Banach contraction principle and Krasnoselskii's fixed point theorem, have been employed to explore the existence and uniqueness of solutions for several nonlinear FODEs such as the implicit FODEs [35], the fractional-order Cauchy problems [36].…”

Attainability to Solve Fractional Differential Inclusion on the Half Line at Resonance

“…In the existence and uniqueness fields, there are many articles concerned with different types of fractional differential equations or inclusions. For fractional differential equations, there are a huge number of contributions (see [4][5][6][7][8][9] and the references given therein). For fractional differential inclusions, Salem and Al-Dosari [10] have studied the existence results of solution for fractional SturmLiouville inclusion associated with composition with multimaps.…”