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arXiv · 1907.04538

Generalized substantial fractional operators and well-posedness of Cauchy problem

Hafiz Muhammad Fahad·Mujeeb ur Rehman
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Abstract

In this work we focus on substantial fractional integral and differential operators which play an important role in modeling anomalous diffusion. We introduce a new generalized substantial fractional integral. Generalizations of fractional substantial derivatives are also introduced both in Riemann-Liouville and Caputo sense. Furthermore, we analyze fundamental properties of these operators. Finally, we consider a class of generalized substantial fractional differential equations and discuss the existence, uniqueness and continuous dependence of solutions on initial data.

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Hafiz Muhammad Fahad, Mujeeb ur Rehman. 2019-07-10. Generalized substantial fractional operators and well-posedness of Cauchy problem. https://arxiv.org/abs/1907.04538

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