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In this paper, we investigate the approximate controllability for fractional integrodifferential inclusions of order r ∈ (1 , 2) in Banach space with sectorial operators. In particular, we obtain a new set of sufficient conditions for the approximate controllability of nonlinear fractional integrodifferential inclusions of order r ∈ (1 , 2) under the assumption that the corresponding linear system is approximately controllable. In addition, we establish the approximate controllability results for the Sobolev type fractional control system with nonlocal conditions. The results are obtained with the help of fractional derivatives, sectorial operators of type (P , η , r , γ) , multivalued functions, and Bohnenblust-fixed Karlin's point theorem. Moreover, an example is also provided to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

• Conformable 3D Wazwaz-Benjamin-Bona-Mahony (3D-WBBM) equation is studied. • A variety of nonlinear dynamical solitary wave structures are extracted. • Bell shaped, shock, singular and multiple soliton are reported. • Generalized exponential rational function method (GERFM) is considered. • The physical characterization of results graphically in 3D, 2D are figured out. In this article, we elucidate the dynamical behavior of exact solitary waves to the conformable 3D Wazwaz-Benjamin- Bona-Mahony (3D-WBBM) equation emerging in shallow water waves. A variety of nonlinear dynamical solitary wave structures are extracted in different shapes like hyperbolic, trigonometric, and exponential function solutions including some special known solitary wave solution like bell shaped, shock, singular and multiple soliton by an analytical mathematical tool namely the generalized exponential rational function method (GERFM). Besides, we also secure singular periodic wave solutions with unknown parameters. All the secured solutions are verified by substituting back to the original equation through soft computation Mathematica. The outcomes show that the governing model theoretically possesses extremely rich structures of exact solitary wave solutions. The physical characterization of some reported results are figured out graphically in 3D, 2D and their corresponding contour profiles by selecting appropriate values of parameters. [ABSTRACT FROM AUTHOR]