Browsing by Author "Djamila Chergui"
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Item Existence and Uniqueness for Multi-Term Sequential Fractional Integro-Differential Equations with Non-Local Boundary Conditions(2021-05-01) Djamila Chergui: In this paper we present a new type of non-local multi-point boundary value problems of Caputo type sequential fractional integro-differential equations. The paper shows that existence and uniqueness results can be obtained using standard tools of fixed point theorem. An application to illustrate the power of the obtained results on quantum information theory is discussed.Item Existence and uniqueness of solutions for nonlinear fractional di erential equations depending on lower-order derivative with non-separated type integral boundary conditions(2019-02-11) Djamila CherguiAbstract: We study a new class of boundary value problems of nonlinear fractional di erential equations whose nonlinear term depends on a lower-order derivative with fractional non-separated type integral boundary conditions. Some existence and uniqueness results are obtained by using standard fixed point theorems. Examples are given to illustrate the results.Item Existence and uniqueness of solutions to higher order fractional partial differential equations with purely integral conditions(2022-05-07) Djamila CherguiAbstract: In this paper, we prove the existence and uniqueness of Caputo time fractionalpseudo-hyperbolic equationsof higher order with purely nonlocal conditions of integral type.We use an a priori estimate method; theso-called energy inequalities method, based on some functional analysis tools, is developed for a Caputo time fractionalof 2m-th and (2m + 1)-thorder and the density of the range of the operator generated by the considered problem. Using the Laplace transform and homotopy perturbation, wefind a semi-analyticalsolution. Finally, we give some examples for illustration.