Well-posedness and stability for a differential problem with Hilfer-Hadamard fractional derivative

DOI10.1155/2013/605029zbMath1470.34017OpenAlexW2140658868WikidataQ58917280 ScholiaQ58917280MaRDI QIDQ2318878

Mohammed D. Kassim, Nasser-eddine Tatar

Publication date: 16 August 2019

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/605029

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Fractional ordinary differential equations (34A08)

Related Items (33)

Theory of fractional hybrid problems in the frame of \(\psi\)-Hilfer fractional operators ⋮ Mixed nonlocal boundary value problem for implicit fractional integro-differential equations via \(\psi\)-Hilfer fractional derivative ⋮ On the existence and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative ⋮ Unnamed Item ⋮ On some fractional differential inclusions with random parameters ⋮ Nonexistence of global solutions for a fractional differential problem ⋮ Coupled systems of Hilfer fractional differential inclusions in Banach spaces ⋮ Nonexistence results of Caputo-type fractional problem ⋮ A qualitative study on generalized Caputo fractional integro-differential equations ⋮ Stability of solutions for generalized fractional differential problems by applying significant inequality estimates ⋮ Unnamed Item ⋮ Stability of logarithmic type for a Hadamard fractional differential problem ⋮ Some Existence and Stability Results of Hilfer-Hadmard Fractional Implicit Differential Equation in a Weighted Space ⋮ A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability ⋮ Nonexistence results for a sequential fractional differential problem ⋮ ON HADAMARD FRACTIONAL CALCULUS ⋮ The existence and Ulam-Hyers stability results for \(\psi\)-Hilfer fractional integrodifferential equations ⋮ Coupled Hilfer fractional differential systems with random effects ⋮ Implicit coupled Hilfer-Hadamard fractional differential systems under weak topologies ⋮ An existence theorem for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions ⋮ Existence and Ulam stability for fractional differential equations of Hilfer-Hadamard type ⋮ Unnamed Item ⋮ Nonexistence of global solutions for fractional differential problems with power type source term ⋮ Fractional differential inclusions of Hilfer type under weak topologies in Banach spaces ⋮ Nonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative ⋮ On Hilfer fractional difference operator ⋮ Existence of solutions of generalized fractional differential equation with nonlocal initial condition ⋮ Hilfer and Hadamard coupled Volterra fractional integro-differential systems with random effects ⋮ Terminal value problem for differential equations with Hilfer-Katugampola fractional derivative ⋮ Coupled Hilfer and Hadamard random fractional differential systems with finite delay in generalized Banach spaces ⋮ Controllability results for Sobolev type \(\psi\)-Hilfer fractional backward perturbed integro-differential equations in Hilbert space ⋮ On Stability of Generalized Cauchy-type Problem ⋮ Existence and Ulam stability results of a coupled system for terminal value problems involving \(\psi\)-Hilfer fractional operator

Cites Work

• On a differential equation involving Hilfer-Hadamard fractional derivative
• Mellin transform analysis and integration by parts for Hadamard-type fractional integrals
• Long time behavior for a nonlinear fractional model
• Existence and uniqueness of solutions for the Cauchy-type problems of fractional differential equations
• A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
• Inequalities for differential and integral equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Power-type estimates for a nonlinear fractional differential equation
• Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions
• On the stability of some fractional-order non-autonomous systems
• Weighted Cauchy-type problem of a functional differ-integral equation
• NONLINEAR DIFFERENTIAL EQUATIONS WITH MARCHAUD‐HADAMARD-TYPE FRACTIONAL DERIVATIVE IN THE WEIGHTED SPACE OF SUMMABLE FUNCTIONS
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