On the existence of solutions of fractional integro-differential equations

By Asadollah Aghajani, Yaghoub Jalilian, Juan Trujillo. Fractional Calculus and Applied Analysis, 2011

104 citations recorded by the source corpus.

Under some suitable conditions, we prove the solvability of a large class of nonlinear fractional integro-differential equations by establishing some fractional integral inequalities and using the nonlinear alternative Leray-Schauder type. The uniqueness of solutions is also proved in some situations.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e7212b8a4bdeeef38323170b475a4eaa2d88a4db

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions (2012, background): “In addition to BVPs for ordinary differential equations, fractional differential inclusions [6, 7, 8], fractional integro-differential equations [2], fractional partial differential equations [3], and the numerical solution of such problems [12] are gaining increasing attention in the literature.”
On the existence and stability for noninstantaneous impulsive fractional integrodifferential equation (2018, background): “Therefore, from Equation(16), we conclude that d(Ωg,Ωh) ≤ Φd(g, h) for all g, h ∈ X, provided the condition given by Equation 11.”
A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations (2014, background): “For some recent development on the topic, see [1], [2], [4], [5], [6], [7], [8], [9], [10], [11], [12], [14], [17], and the references therein.”
Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces (2013, background): “Recently, the first and third authors and Jalilian [2] proved the solvability of a large class of nonlinear fractional integro-differential equations by establishing some fractional integral inequalities and using the nonlinear alternative of Leray-Schauder type.”
Monotone iterative method for a class of nonlinear fractional differential equations (2012, background): “The range of applications of the fractional calculus is very large at this moment and it is expected to increase in the nearest future (see for example [14],[11],[3],[5],[2],[1] and the references therein).”