Advances in Boundary Value Problems for Fractional Differential Equations

• Other Authors: Luca, Rodica (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: Information technology industries; Computer science; piecewise constant function; Mawhin's continuation technique; variable order; resonance; existence; time-fractional damped wave inequalities; bounded domain; singularity; nonexistence; Riemann-Liouville fractional differential equations; nonlocal boundary conditions; singular functions; positive solutions; multiplicity; coincidence degree theory; four-point boundary value problem system; at resonance; fractional evolution systems; approximate controllability; Sobolev operator; compactness; Schauder fixed point theorem; sequential fractional differential equations; Caputo fractional derivative; Riemann-Stieltjes integro-multipoint boundary conditions; existence and uniqueness; fixed point; fractional calculus; fractional differential equation; boundary value problem; Chebyshev polynomial; collocation method; impulsive fractional differential inclusions; neutral differential inclusions; mild solutions; contractible sets; Rδ-set; boundary value problems; fractional q-difference equations; Caputo fractional q-difference derivative; measure of noncompactness; Mönch's fixed point theorem; nonlocal coupled boundary conditions; positive parameters; resolvent operator; delay; nonlocal conditions; parameter; fractional integro-differential equation; Sturm-Liouville boundary condition; variational method; Hilfer fractional system; neutral system; multi-valued maps; sectorial operators; fractional Dzhrbashyan-Nersesyan derivative; differential equation with fractional derivatives; resolving family of operators; perturbation theorem; initial value problem; initial-boundary value problem; viscoelastic Oldroyd fluid; q-calculus; fractional q-integro-difference system; solvability; Riemann-Stieltjes q-integrals; fixed point theorems; n/a
• Online Access: DOAB: download the publication; DOAB: description of the publication

This reprint covers new aspects of the recent developments in the theory and applications of fractional differential equations, including inclusions, inequalities, and systems of fractional differential equations with Riemann-Liouville derivatives, Caputo derivatives, or other generalized fractional derivatives, subject to various boundary conditions. The authors study the existence, uniqueness, multiplicity, and nonexistence of classical or mild solutions, the approximation of solutions, and the approximate controllability of mild solutions for diverse mathematical models.