Abstract
We study the existence and uniqueness theorem for the nonlinear fractional mixed Volterra-Fredholm integrodifferential equation with nonlocal initial condition , where , , and is a given function. We point out that such a kind of initial conditions or nonlocal restrictions could play an interesting role in the applications of the mentioned model. The results obtainded are applied to an example.
Highlights
It have been proved that the differential models involving nonlocal derivatives of fractional order arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in many fields, for instance, physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, and so forth see 1– 6
A real function f t is said to be in the space Cα, α ∈ R if there exists a real number p > α, such that f t tpg t, where g ∈ C 0, ∞, while f t is said to be in the space Cαm if and only if f m ∈ Cα, m ∈ N
We obtain the following lemmas to prove the main results on the existence of solutions to 1.2
Summary
It have been proved that the differential models involving nonlocal derivatives of fractional order arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in many fields, for instance, physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, and so forth see 1– 6. Such models can be considered as an efficient alternative to the classical nonlinear differential models to simulate many complex processes see 7. Very recently N’Guerekata 2, 18 discussed the existence of solutions of fractional abstract differential equations with nonlocal initial condition.
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