An approach via fractional analysis to non-linearity induced by coarse-graining in space

Positive solutions for a semipositone fractional boundary value problem with a forcing term

“…The monographs [14,19] and the papers [13,16,18,20] are excellent sources for the theory and applications of fractional calculus. Among all the topics, the existence of positive solutions of BVPs of fractional differential equations has been extensively studied by many researchers in recent years; see, for example, [1,2,3,6,7,8,9,11,21,23] and the references therein.…”

Fractional derivatives in spaces of generalized functions

“…[4], [11], and references therein) as well as a new topic (cf. [10], [7], [20], [5], [8], [6], [9], [17] among the others). The main disadvantage of this calculus up to now, is the lack of appropriate functional spaces for their investigations.…”

Fractional calculus of variations for a combined Caputo derivative

“…Since then, the new theory turned out to be very attractive to c 2011 Diogenes Co., Sofia pp. 523-537 , DOI: 10.2478/s13540-011-0032-6 mathematicians and many different forms of fractional operators were introduced: the Grunwald-Letnikov, Riemann-Liouville, Riesz, and Caputo fractional derivatives (see, e.g., [25,35,40]), and the more recent notions of [26], [15], and [23,24]. Besides in mathematics, fractional derivatives and integrals appear in physics, mechanics, engineering, elasticity, dynamics, control theory, economics, biology, chemistry, etc.…”

“…[9,13,31,37] and references therein). The FC theory and applications are nowadays presented in several books (e.g., [22,25,30,33,35,40]) and in a large number of relevant papers (see, e.g., [2,6,11,20,23,24,26,36,42] and many others in this journal "Fract. Calc.…”