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Fractional Differential Equations, Inclusions and Inequalities with Applications
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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, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.
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Keywords
- anti-periodic boundary value problems
- arbitrary order differential equations
- boundary value problem
- Caputo fractional derivative
- Caputo-type fractional derivative
- Caputo–Fabrizio fractional differential equations
- Caputo’s fractional derivative
- condensing multivalued map
- conformable derivative
- conformable double Laplace decomposition method
- conformable fractional calculus
- conformable Laplace transform
- conformable partial derivative
- continuous dependence
- convergence estimates
- Convex function
- Convex functions
- coupled system
- coupled system of fractional difference equations
- differential inclusions
- discrete half-line
- distributed delay
- existence
- existence and uniqueness of solution
- existence of solutions
- existence theory
- exponential kernel
- exponentially convex function
- fixed point
- fixed point theorem
- fixed-point theorems
- fractal space
- fractional bennett’s inequality
- Fractional calculus
- fractional copson’s inequality
- fractional derivative
- fractional derivatives
- fractional differential equation
- fractional differential inclusions
- fractional evolution inclusions
- fractional hardy’s inequality
- fractional hölder inequality
- fractional integral
- fractional integral inequalities
- fractional integrals
- fractional leindler’s inequality
- fractional q-difference inclusion
- fractional sum
- fractional sum-difference equations
- functional fractional differential inclusions
- generalized fractional integral
- generalized Liouville–Caputo derivative
- generalized Riemann-liouville fractional integrals
- Green function
- Green’s function
- Hadamard fractional derivative
- hadamard proportional fractional integrals
- Hermite–Hadamard inequalities
- Hermite–Hadamard inequality
- Hermite–Hadamard type inequalities
- Hermite–Hadamard-type inequalities
- HU stability
- Hyers–Ulam stability
- ill-posed problem
- impulses
- inequalities
- integral representation
- integro-multipoint boundary conditions
- interval-valued functions
- inverse problem
- iterative method
- Katugampola fractional integrals
- Langevin equation
- Mathematics & science
- Matrix theory
- measure of noncompactness
- mild solutions
- multiple positive solution
- neutral fractional systems
- non-instantaneous impulsive equations
- nonlocal
- nonlocal boundary conditions
- nonlocal fractional delta-nabla sum boundary value problem
- Ostrowski type inequality
- Perov-type fixed point theorem
- positive solution
- positive solutions
- positivity of solution
- proportional fractional integrals
- q-integro-difference equation
- Qi inequality
- random impulsive and junction points
- Reference, information & interdisciplinary subjects
- Research & information: general
- Riemann-Liouville fractional integral
- Riemann–Liouville fractional integrals
- Riemann–Liouville type fractional problem
- s-convex function
- sequential fractional delta-nabla sum-difference equations
- singular one dimensional coupled Burgers’ equation
- solution
- Stability Theory
- the index of fixed point
- the method of lower and upper solutions
- three-point boundary-value problem
- time-fractional diffusion equation
- Timescales
- Ulam-Hyers stability
- Uniqueness
- ψ-Riesz-Caputo derivative
Links
DOI: 10.3390/books978-3-03943-219-6Editions