EXISTENCE OF SOLUTIONS OF FRACTIONAL EQUATION WITH NEW BOUNDARY CONDITIONS

Karima Ali Khelil     (Badji Mokhtar University, Mathematics Department, Laboratory LANOS, B.P. 12, Annaba, 23000, Algeria)
Chahrazed Messikh     (Badji Mokhtar University, Mathematics Department, Laboratory LANOS, B.P. 12, Annaba, 23000, Algeria)

Abstract


In this paper, we investigate a nonlinear fractional integro-differential equation involving Caputo fractional derivatives together with nonlocal boundary conditions. In contrast to some existing works, the problem is considered with homogeneous initial conditions. By applying Krasnoselskii's fixed-point theorem together with the Arzelá–Ascoli theorem, we establish sufficient conditions ensuring the existence of solutions in an appropriate Banach space. The obtained results extend and complement earlier contributions in the literature. An example is provided to illustrate the theory.


Keywords


Integro-differential equations, Boundary value problem, Fractional integral operator, Fractional derivative operator

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References


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DOI: http://dx.doi.org/10.15826/umj.2026.1.001

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