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

Abstract

The presented article is deduced about the positive solutions of the fractional differential inclusion at resonance on the half line. The fractional derivative used is in the sense of Riemann–Liouville and the problem is supplemented by unseparated conditions. The existence results are illustrated in view of Leggett–Williams theorem due to O’Regan and Zima on unbounded domain.

Solvability of a Hadamard Fractional Boundary Value Problem at Resonance on Infinite Domain

“…To the best of our knowledge, there are few papers that have investigated the boundary value problems of Hadamard fractional differential equations at resonance on infinite domain. Inspired by the excellent results in [18][19][20][21], we will discuss this problem by constructing two suitable Banach spaces, establishing an appropriate compactness criterion, defining appropriate operators and the coincidence degree theory due to Mawhin. In this paper, we will assume that the following conditions hold.…”

Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space

“…There is a clear progress on fractional Langevin equations in physics [15][16][17][18][19]. New results on the existence of solutions for fractional Langevin equations under variety of boundary value conditions have been published; see [20][21][22][23][24][25][26][27][28][29] and the references mentioned therein.…”

Compact and Noncompact Solutions to Generalized Sturm–Liouville and Langevin Equation with Caputo–Hadamard Fractional Derivative

“…In particular, the FoDEs played and still play a significant role in developing lots of models that outline several engineering problems and physical applications such as electromagnetics, porous media, control, and viscoelasticity [3]. For further facts on the basic principles of fractional calculus and the FoDEs, the reader may return to the references [4][5][6][7]. e fractional calculus, new interesting research field, is attracting the interest of mathematicians and researchers.…”