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Our aim in the present research article is to discuss some existence aspects of solutions for two given fractional q‐sequential structures of an integro‐differential BVP in which the R.H.S. nonlinear term is regarded as two functions in both single‐valued and multivalued versions. In addition to this, we formulate the boundary conditions in the framework of the mixed q‐integro‐derivative conditions simultaneously. For such new fractional q‐sequential integro‐differential structures, we utilize suitable standard analytical methods attributed to Krasnoselskii on the sum of two operators. In the final stage, we design two simulative examples to check the consistency of findings in the context of the proposed techniques. [ABSTRACT FROM AUTHOR]

In the current research, we derive some existence and stability criteria for two hybrid and non‐hybrid differential equations of fractional order. By utilizing an analytical technique based on the generalized Dhage's fixed point result, we verify desired existence theorem for the hybrid problem. Also, we consider a special case as a non‐hybrid problem and by using the Kuratowski's measure of non‐compactness, we establish a new existence criterion. Eventually, we turn to investigation of the stability of solutions for the non‐hybrid problem by applying the generalized Gronwall's inequality. Finally, we provide an example to illustrate the relevant non‐hybrid result. [ABSTRACT FROM AUTHOR]

In the present research manuscript, we introduce a novel general fractional boundary value inclusion problem and investigate the necessary and sufficient conditions for desired existence results. Indeed, more precisely, we formulate a class of fractional multiterm Caputo–Hadamard differential inclusion problem with two‐point sum boundary value conditions. In two separate theorems, we prove the existence results for mentioned inclusion problem by using α‐ψ‐contractive maps and approximate endpoint property. Finally, we provide an example to illustrate our main results. [ABSTRACT FROM AUTHOR]

In the current paper, we intend to check the existence aspects of solutions for a category of the multi‐point boundary value problem (BVP) involving a p$$ p $$‐Laplacian differential operator within the generalized fractional derivatives depending on another function. Based on two fixed point results attributed to Schaefer and Banach, the desired results are verified. Further, the continuity of solutions in terms of inputs (fractional orders, associated parameters, and appropriate function) is extensively discussed. A simulative example is prepared to demonstrate the applications of the obtained results. [ABSTRACT FROM AUTHOR]

The development of laser‐based cooling and spectroscopic methods has produced unprecedented growth in the ion trapping industry. Mathieu equation, a differential equation with periodic coefficients, is employed to develop models of ion motions under the influence of fields. Ion traps with octopole field is described with nonlinear Mathieu equation with cubic term. This article aims at considering motion of ions under the electric potential with negative octopole field with damping caused by the collision of the ions with Helium buffer gas modeled with tempered fractional derivative. Schaefer's fixed point theorem and Banach's contraction principle are employed to establish the existence of unique solution for the considered tempered fractional nonlinear Mathieu equation model of an ion motion. Further, the analysis of stability is performed in the sense of Hyers and Ulam. The feasibility of the obtained theoretical results are numerically confirmed for suitable parametric values, and simulations are performed supporting them. [ABSTRACT FROM AUTHOR]