Existence and Uniqueness of the Mild Solution of an Abstract Semilinear Fractional Differential Equation with State Dependent Nonlocal Condition

DOI10.46793/KgJMat2106.909HMaRDI QIDQ5035252

Ashraf H. A. Radwan, Mohamed A. E. Herzallah

Publication date: 21 February 2022

Published in: Kragujevac Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://elib.mi.sanu.ac.rs/files/journals/kjm/68/6_eng.html

zbMATH Keywords

\(C_0\)-semigroupsKrasnoselskii's fixed point theoremCaputo derivativecontinuous dependence\(\epsilon\)-approximate solutionstate dependent nonlocal condition

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Nonlinear differential equations in abstract spaces (34G20) Nonlocal and multipoint boundary value problems for ordinary differential equations (34B10) Fractional ordinary differential equations (34A08)

Related Items (2)

Existence and uniqueness of mild solutions for mixed Caputo and Riemann-Liouville semilinear fractional integrodifferential equations with nonlocal conditions ⋮ Mild solution to hybrid fractional differential equations with state-dependent nonlocal conditions

Cites Work

• Unnamed Item
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• Solutions of a class of deviated-advanced nonlocal problems for the differential inclusion \(x'(t)\in F(t,x(t))\)
• A class of fractional evolution equations and optimal controls
• On approximate solutions for a class of semilinear fractional-order differential equations in Banach spaces
• Nonlocal Cauchy problem for fractional evolution equations
• A generalized Gronwall inequality and its application to a fractional differential equation
• Existence of mild solutions for fractional neutral evolution equations
• Fractional dynamics. Applications of fractional calculus to dynamics of particles, fields and media
• Semigroups of linear operators and applications to partial differential equations
• Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions
• On state dependent non-local conditions
• On abstract differential equations with state dependent non-local conditions
• Fractional thermoelasticity
• Fixed Point Theorems and Their Applications
• The Fractional Trigonometry
• Basic Theory of Fractional Differential Equations
• Fractional diffusion: probability distributions and random walk models

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