Fractional Differential Equations, Inclusions and Inequalities with Applications

• Other Authors: Ntouyas, Sotiris K. (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: Research & information: general; Mathematics & science; fractional evolution inclusions; mild solutions; condensing multivalued map; arbitrary order differential equations; multiple positive solution; Perov-type fixed point theorem; HU stability; Caputo fractional derivative; nonlocal; integro-multipoint boundary conditions; existence; uniqueness; Ulam-Hyers stability; coupled system of fractional difference equations; fractional sum; discrete half-line; non-instantaneous impulsive equations; random impulsive and junction points; continuous dependence; Caputo-Fabrizio fractional differential equations; Hyers-Ulam stability; fractional derivative; fixed point theorem; fractional differential equation; fractional sum-difference equations; boundary value problem; positive solution; green function; the method of lower and upper solutions; three-point boundary-value problem; Caputo's fractional derivative; Riemann-Liouville fractional integral; fixed-point theorems; Langevin equation; generalized fractional integral; generalized Liouville-Caputo derivative; nonlocal boundary conditions; fixed point; fractional differential inclusions; ψ-Riesz-Caputo derivative; existence of solutions; anti-periodic boundary value problems; q-integro-difference equation; fractional calculus; fractional integrals; Ostrowski type inequality; convex function; exponentially convex function; generalized Riemann-liouville fractional integrals; convex functions; Hermite-Hadamard-type inequalities; exponential kernel; caputo fractional derivative; coupled system; impulses; existence theory; stability theory; conformable derivative; conformable partial derivative; conformable double Laplace decomposition method; conformable Laplace transform; singular one dimensional coupled Burgers' equation; Green's function; existence and uniqueness of solution; positivity of solution; iterative method; Riemann-Liouville type fractional problem; positive solutions; the index of fixed point; matrix theory; differential inclusions; Caputo-type fractional derivative; fractional integral; time-fractional diffusion equation; inverse problem; ill-posed problem; convergence estimates; s-convex function; Hermite-Hadamard inequalities; Riemann-Liouville fractional integrals; fractal space; functional fractional differential inclusions; Hadamard fractional derivative; Katugampola fractional integrals; Hermite-Hadamard inequality; fractional q-difference inclusion; measure of noncompactness; solution; proportional fractional integrals; inequalities; Qi inequality; caputo-type fractional derivative; fractional derivatives; neutral fractional systems; distributed delay; integral representation; fractional hardy's inequality; fractional bennett's inequality; fractional copson's inequality; fractional leindler's inequality; timescales; conformable fractional calculus; fractional hölder inequality; sequential fractional delta-nabla sum-difference equations; nonlocal fractional delta-nabla sum boundary value problem; hadamard proportional fractional integrals; fractional integral inequalities; Hermite-Hadamard type inequalities; interval-valued functions
• Online Access: DOAB: download the publication; DOAB: description of the publication

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, visc...