scientific article

zbMath1111.26011MaRDI QIDQ3024737

Hussein A. H. Salem, Ahmed M. A. El-Sayed

Publication date: 5 March 2007

Full work available at URL: https://eudml.org/doc/31966

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zbMATH Keywords

Cauchy problemfractional calculuspseudo solution

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Fractional derivatives and integrals (26A33) Integral operators (47G10)

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Weak and pseudo-solutions of an arbitrary (fractional) orders differential equation in nonreflexive Banach space ⋮ On the theory of fractional calculus in the Pettis-function spaces ⋮ Multi-term fractional differential equations in a nonreflexive Banach space ⋮ Weak solutions for fractional differential equations in nonreflexive Banach spaces via Riemann-Pettis integrals ⋮ Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus ⋮ Fractional calculus and fractional differential equations in nonreflexive Banach spaces ⋮ Unnamed Item ⋮ On the weak solution $u ∈ C_1-α(I,E) of a fractional-order weighted Cauchy type problem in reflexive Banach spaces ⋮ Hadamard-type fractional calculus in Banach spaces ⋮ On functions without pseudo derivatives having fractional pseudo derivatives ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Fixed-point theory for weakly sequentially continuous mappings
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Ideal spaces
• Solutions of differential equations in B-spaces
• An abstract Gronwall lemma and applications to global existence results for functional differential and integral equations of fractional order
• Geometry and the Pettis Integral
• On the existence of weak solutions of differential equations in nonreflexive banach spaces
• A Global Existence and Uniqueness Theorem for Ordinary Differential Equations of Generalized Order
• Nonlinear functional differential equations of arbitrary orders
• Pettis Integration
• Some existence theorems on differential equations of generalized order.
• On Integration in Vector Spaces
• Integration in a Convex Linear Topological Space
• Set-valued integral equations of fractional-orders
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