Abstract
This research article is mainly concerned with the existence of solutions for a coupled Caputo–Hadamard of nonconvex fractional differential inclusions equipped with boundary conditions. We derive our main result by applying Mizoguchi–Takahashi’s fixed point theorem with the help of mathcal{P}-function characterizations.
Highlights
In the previous two decades, fractional calculus has earned sizeable importance owing to diverse applications in scientific and engineering problems
Fractional-order boundary value problems, in particular, have became a rapidly growing area due to features of fractional derivatives which make the systems of fractional-order practical and realistic than the corresponding classical systems
There are numerous definitions of fractional differentiation operators in the literature, the most common is the classical Riemann–Liouville type fractional derivative after which a beneficial alternative has been introduced to cope with disadvantages caused by the Riemann– Liouville expression, the so-called Caputo derivative
Summary
In the previous two decades, fractional calculus has earned sizeable importance owing to diverse applications in scientific and engineering problems. Fractional-order boundary value problems, in particular, have became a rapidly growing area due to features of fractional derivatives which make the systems of fractional-order practical and realistic than the corresponding classical systems. There are numerous definitions of fractional differentiation operators in the literature, the most common is the classical Riemann–Liouville type fractional derivative after which a beneficial alternative has been introduced to cope with disadvantages caused by the Riemann– Liouville expression, the so-called Caputo derivative. Fractional derivatives within the frame of Hadamard type differ from the Riemann–Liouville type and the Caputo type due to the appearance of a logarithmic function in the definition of the Hadamard derivatives. One can find manifold monographs and articles devoted exclusively to the theory of fractional derivatives, not merely on mathematical subjects and physics, applied sciences, engineering, etc.; see [11,12,13,14]
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