Perturbation for fractional-order evolution equation |
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Authors: | Mohamed A E Herzallah Ahmed M A El-Sayed Dumitru Baleanu |
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Institution: | 1.Faculty of Science,Zagazig University,Zagazig,Egypt;2.Faculty of Science,Alexandria University,Alexandria,Egypt;3.Department of Mathematics and Computer Science,?ankaya University,Ankara,Turkey;4.Institute of Space Sciences,Magurele-Bucharest,Romania |
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Abstract: | Fractional calculus has gained a lot of importance during the last decades, mainly because it has become a powerful tool in
modeling several complex phenomena from various areas of science and engineering. This paper gives a new kind of perturbation
of the order of the fractional derivative with a study of the existence and uniqueness of the perturbed fractional-order evolution
equation for CDa-e0+u(t)=A CDd0+u(t)+f(t),^{C}D^{\alpha-\epsilon}_{0+}u(t)=A~^{C}D^{\delta}_{0+}u(t)+f(t),
u(0)=u
o
, α∈(0,1), and 0≤ε, δ<α under the assumption that A is the generator of a bounded C
o
-semigroup. The continuation of our solution in some different cases for α, ε and δ is discussed, as well as the importance of the obtained results is specified. |
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Keywords: | |
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