The existence of positive solutions is established for boundary value problems defined within generalized Riemann-Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green functions and study their properties for three different types of boundary value problems. Examples are presented to demonstrate the validity of theoretical findings.

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In this paper, we consider the newly defined partial (?,?)-fractional integral and derivative to study a new class of partial fractional differential equations with impulses. The existence and Ulam-Hyers stability of solutions for the proposed equation are investigated via the means of measure of noncompactness and fixed point theorems. The presented results are quite general in their nature and further complement the existing ones.

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The main purpose of this work is to establish existence result and stability criteria for a class of fractional order differential equations using fixed point theorems. Existence results are based on Schauder's fixed point theorem, Banach contraction principle and, emphasis is put on the application of the Krasnoselskii's fixed point theorem to establish stability criteria of a specific class of fractional order differential equations. An example is given to show the usefulness of the stability result.